Nonlinear science Books

Book SynopsisThis book provides new research on the advances in non-linear dynamics. Chapter One studies compactions in carbon nanotube arrays. Chapter Two reviews the elastic and plastic type behaviours in the Fractal Theory of Motion at nanoscale. Chapter Three analyses a particular model of tumour progression, assuming that the invasive cells, the connective tissue and the proteases are moving through a non-differential medium governed by the Non-Standard Scale Relativity Theory (NSRT) (Scale Relativity Theory with arbitrary constant fractal dimension). Chapter Four studies the process of drug release from a polymer matrix. Chapter Five examines the implications of drug release from a polymeric matrix process. Chapter Six reviews behaviours of travelling waves and Shapiro step types in a tumour-growth model. Chapter Seven discusses the astonishing evolutionary dynamics of a class of nonlinear discrete 2D pattern formations and growth models.

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Book SynopsisNon-linear, or chaotic behaviour in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. Applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena. This book presents important new research in this dynamic field.

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Book SynopsisThis book focuses on recent and significant research on non-linear, or chaotic behaviour which in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. Applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena.

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Book SynopsisNon-linear analysis is a broad, interdisciplinary field characterised by a mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This book presents recent and important research in the field.

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Book SynopsisWith the rapid development of science and technology, the computer has become an important tool in many science fields. Particularly, symbolic computation, which is one of the most exciting and challenging areas. It has been applied in many sciences such as mathematics, physics, chemistry, biology, mechanics, engineering, etc., in particular, non-linear sciences ad complex sciences. Nowadays, many symbolic computation softwares have been used to deal with these problems. Up to now, there have existed many non-linear differential/difference systems related to solitons and chaos in the non-linear science field. In order to understand these complex physical phenomena, it is important to research some of their basic properties. Because of the complexity of these non-linear systems, with the symbolic computation, this new book presents important research on non-linear differential/difference systems, related to solitons and chaos as well as other non-linear sciences in views of constructive algorithms.

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Book SynopsisProvides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation.

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Book SynopsisAtomically scaled “smart” devices, artificial intelligence, neuromorphic functions, alternative logic operations and computing, new memory storage paradigms, ultra-fast/bio-inspired/flexible/transparent/energy-efficient nanoelectronics – these contemporary concepts are driving forces for the progressive development of science and technology, mirroring societal expectations and solving its problems. Inspired by the concept of the memristor (memory + resistor), Redox-based resistive switching Random Access Memories (ReRAM) and Phase Change Memories (PCM) are thought capable of all these operations and functionalities. In addition, researchers aim to use these memristive systems to enable the fundamental properties of life, including order, plasticity, response to stimuli, metabolism, homeostasis, growth, and heredity or reproduction, based on the functionalities of biological systems. This volume, which brings together experts from industry and academia, will cover the fundamentals as well as specific demands and limitations in e.g. materials selection, processing, suitable model systems, technical requirements and the potential device applications, providing a bridge for terminologies, theories, models, and applications. The topics covered in this volume include: Electrochemical metallization ReRAMs (ECM) Valence change ReRAMs (VCM) Phase-change memories (PCM) Synaptic and neuromorphic functionsTable of ContentsElectrochemical metallization ReRAMs (ECM); Valence change ReRAMs (VCM); Phase-change memories (PCM); Synaptic and neuromorphic functions

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Book SynopsisUsing models, developed in one branch of science, to describe similar behaviors encountered in a different one, is the essence of a synergetic approach.A wide range of topics has been developed including Agent-based models, econophysics, socio-economic networks, information, bounded rationality and learning in economics, markets as complex adaptive systems — evolutionary economics, multiscale analysis and modeling, nonlinear dynamics and econometrics, physics of risk, statistical and probabilistic methods in economics and finance.This publication concentrates on process behavior of economic systems and building models that stem from Haken's, Prigogine's, Taylor's work as well as from nuclear physics models.Table of ContentsBifurcation Theory Application - The Use of Child Labor in Low Income Economies; Second Order Effects in Population Migration - Reversing Trends; Cities as Reactors of Economic Transactions; Optimality and Chaotic Behavior in Unbundled Energy Markets; Fokker - Planck Equation and the Decision to Support or Abandon Technology Penetration; Nonlinear Effects in Technological Knowledge Production; Institutions as Benard-Taylor Dynamically Stable Processes; Final Thoughts on a Different Way to Look at Economic Processes.

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Book SynopsisThis book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book.Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model is then introduced, which captures a thermodynamic phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values.Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, not constrained by having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that the repeated application of simple rules may spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics.Visit for animations for the models in the book (available for Windows and Linux), solutions to exercises, as well as a list with corrections.Trade Review"Personally, I enjoyed reading this book very much. The arguments are clear and draw attention to a number of useful insights ... Students will find the presentation on self-organized criticality fun to read, particularly because it deals with real phenomena, such as earthquakes, rice-pile avalanches and rainfall ... I strongly agree with these authors that undergraduates need to be exposed to issues related to complexity and criticality. Their textbook is the first that I have seen that makes developing such courses feasible."Mathematical ReviewsTable of ContentsPercolation: Percolating Phase Transition; In One and Two Dimensions, and in the Bethe Lattice; Geometric Properties of Clusters; Scaling Ansatz, Scaling Functions and Scaling Relations; Universality; Real-Space Renormalisation Group; Ising Model: Review of Thermodynamics and Statistical Mechanics; Symmetry Breaking; Ferromagnetic Phase Transition; In One and Two Dimensions, and in the Mean-Field; Landau Theory of Continuous Phase Transitions; Scaling Ansatz, Scaling Functions and Scaling Relations; Universality; Real-Space Renormalisation Group; Self-Organised Criticality: BTW Model in One and Two Dimensions, and in the Mean-Field; A Rice Pile Experiment and the Oslo Model; Earthquakes and the OFC Model; Rainfall; Self-Organised Criticality as a Unifying Principle.

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Book SynopsisNonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

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Book SynopsisThis book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.Table of ContentsIntroduction.- Fundamental terminology.- Complexity.- Classical versus quantum dynamics.- Problems.- References.- Dynamical systems.- Evolution law.- One-dimensional maps.- Problems.- References.- Nonlinear Hamiltonian systems.- Integrable examples.- Hamiltonian formalism.- Important techniques in the Hamiltonian formalism.- Integrable systems.- Non-integrable systems.- Perturbation of low-dimensional systems.- Canonical perturbation theory.- Transition to chaos in Hamiltonian systems.- Criteria for local and global chaos.- Appendix.- Problems.- References.- Dissipative systems - Introduction - Fixed points - Fixed point scenarios in two dimensional systems - Damped Oscillators - Harmonic oscillator - Nonlinear oscillators - Nonlinear damping - Poincaré-Bendixson Theorem - Damped forced oscillators - Driven one-Dimensional harmonic oscillator - Duffing oscillator - Lorenz model for turbulence - Fractals - Simple examples - Box-counting dimension - Examples from nature - Bifurcation scenarios - Examples of pitchfork bifurcations - Tangent bifurcations - Transcritical bifurcations - Higher-order bifurcations - Hopft bifurcations - Intermittency - Coupled Oscillators - Synchronisation - Kuramoto model - Increasing complexity - Problems - References. -Aspects of quantum chaos.- Introductory remarks on quantum mechanics.- Semiclassical quantization of integrable systems.- Semiclassical description of non-integrable systems.- Wave functions in phase space.- Anderson and dynamical localization.- Universal level statistics.- Concluding remarks.- Appendix.- Problems.- References.- Index.

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Book SynopsisStochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.Table of Contents1 Introduction.- 2 Finite elasticity as prior information.- 3 Are elastic materials like gambling machines?.- 4 Elastic instabilities.- 5 Oscillatory motions.- 6 Liquid crystal elastomers.- 7 Conclusion.- Appendix A Notation.- Appendix B Fundamental concepts.- Bibliography.- Index.

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Book SynopsisProviding readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.Table of Contents1 Introduction to Dynamical Systems.- 2 Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems.- 3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- 4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- 5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems.- 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- 7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems.- 8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- 9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- 10 Numerical Analysis of Bifurcations.- A Basic Notions from Algebra, Analysis, and Geometry.- A.1 Algebra.- A.1.1 Matrices.- A.1.2 Vector spaces and linear transformations.- A.1.3 Eigenvectors and eigenvalues.- A.1.4 Invariant subspaces, generalized eigenvectors, and Jordan normal form.- A.1.5 Fredholm Alternative Theorem.- A.1.6 Groups.- A.2 Analysis.- A.2.1 Implicit and Inverse Function Theorems.- A.2.2 Taylor expansion.- A.2.3 Metric, normed, and other spaces.- A.3 Geometry.- A.3.1 Sets.- A.3.2 Maps.- A.3.3 Manifolds.- References.

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Book SynopsisThe spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.Trade Review“I highly recommend this book for graduate students, researchers interested in the modern developments of dynamical systems theory and quantum chaos. This Fourier analytic approach has already had a deep impact on the subject and is now used widely in other related fields.” (Frédéric Naud, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 122, 2020)Table of Contents​1 Introduction.- Part I Smooth expanding maps.- 2 Smooth expanding maps: The spectrum of the transfer operator.- 3 Smooth expanding maps: Dynamical determinants.- Part II Smooth hyperbolic maps.- 4 Anisotropic Banach spaces dened via cones.- 5 A variational formula for the essential spectral radius.- 6 Dynamical determinants for smooth hyperbolic dynamics.- 7 Two applications of anisotropic spaces.- Part III Appendices.- A Spectral theory.- B Thermodynamic formalism: Non-multiplicative topological pressure.- C Properly supported operators (pseudolocality).- D Alternative proofs for C1 dynamics and weights.- References.- Index.

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Book SynopsisThis textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential. Trade Review“Lynch has successfully captured this: I find this book to be uniquely successful in teaching a branch of mathematics together with computing while inspiring students to look at references and explorations beyond the text.” (Patrick Shipman, SIAM Review, Vol. 62 (2), 2020)“This book is meant as an upper level undergraduate or graduate text in dynamical systems. … this is an attractive text, one that I wish I had access to when I was learning dynamical systems, and one that I would be glad to teach from.” (John Starrett, MAA Reviews, July 28, 2019)Table of ContentsPreface.- A Tutorial Introduction to Python.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincaré Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert's Sixteenth Problem.- Delay Differential Equations.- Linear Discrete Dynamical Systems.- Nonlinear Discrete Dynamical Systems.- Complex Iterative Maps.- Electromagnectic Waves and Optical Resonators.- Fractals and Multifractals.- Image Processing with Python.- Chaos Control and Synchronization.- Neural Networks.- Binary Oscillator Computing.- Coursework and Examination-Type Questions.- Solutions to Exercises.- Index of Python Programs.- Index.

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Book SynopsisDas Buch wendet sich an Leser, die - über die rein computergraphische Darstellung hinaus - an einer analytischen Untersuchung von chaotischen und nichtchaotischen Differenzen- und Differentialgleichungssystemen interessiert sind. Breiter Raum wird der Durchrechnung von Beispielen gegeben. Dargestellt werden zunächst qualitative Methoden als auch solche, die das Auffinden von Attraktoren, Bifurkationen etc. und deren Klassifikation in Abhängigkeit von den Systemparametern gestatten. Der letzte Teil schließlich widmet sich der quantitativen Beschreibung chaotischer Systeme. Dazu werden zuerst die Begriffe Chaos und Fraktal exakt definiert und dann die verschiedenen fraktalen Dimensionen, Lyapunov-Exponenten, Entropien etc. eingeführt und durch Beispiele begründet.Table of Contents1 Einleitung.- 2 Diskrete Systeme.- 2.1 Fixpunkte.- 2.2 Lineare und nichtlineare Abbildungen.- 2.3 Abbildungen mit chaotischem Verhalten.- 2.3.1 Die Bernoulli-Abbildung.- 2.3.2 Die logistische Parabel.- 2.3.3 Die Hénon-Abbildung.- 2.4 Die Poincaré-Abbildung.- Anhang A (Verallgemeinerte Eigenvektoren und Jordan-Formen).- Aufgaben.- 3 Kontinuierliche dynamische Systeme.- 3.1 Definitionen, Existenz- und Eindeutigkeitssätze.- 3.2 Eigenschaften der Lösungen von gewöhnlichen Differentialgleichungen.- 3.2.1 Stabilität von Lösungen.- 3.2.2 Asymptotik.- 3.3 Fixpunkte.- 3.3.1 Stabilität von Fixpunkten.- 3.3.2 Struktur von Lösungen in kleinen Umgebungen von Fixpunkten.- 3.3.3 Klassifikation von Fixpunkten.- 3.3.4 Pendelschwingungen.- 3.4 Hamilton-Systeme.- 3.5 Zentrale Mannigfaltigkeiten.- 3.5.1 Parameterabhängige zentrale Mannigfaltigkeiten.- 3.6 Normalformen.- Aufgaben.- 4 Bifurkationen.- 4.1 Äquivalente und konjugierte dynamische Systeme, strukturelle Stabilität.- 4.2 Verzweigungs-Grundtypen.- 4.3 Die Sattel-Knoten-Bifurkation.- 4.4 Die transkritische Verzweigung.- 4.5 Die Pitchfork-Bifurkation.- 4.6 Die Hopf-Bifurkation.- 4.7 Methode der Projektionen.- 4.8 Stabilität periodischer Lösungen.- Anhang A (Fredholm-Alternative).- Anhang B (Hopf-Bifurkationen in kontinuierlichen Systemen).- Aufgaben.- 5 Asymptotische Methoden.- 5.1 Die Mittelwert-Methode.- 5.2 Beispiele.- 5.3 Schwach nichtlineare Oszillatoren.- 5.4 Die Viel variablen-Methode.- Aufgaben.- 6 Homokline Bifurkationen.- 6.1 Die Standardabbildung.- 6.2 Sattelpunkte flächenerhaltender Abbildungen.- 6.3 Elliptische Fixpunkte flächenerhaltender Abbildungen und KAM-Kurven.- 6.4 Winkel- und Wirkungsvariable.- 6.5 Schwach gestörte Hamilton-Systeme.- 6.6 Das Melnikov-Kriterium.- 6.6.1 Homokline Koordinaten.- 6.6.2 Abstand zwischen stabilen und instabilen Mannigfaltigkeiten gestörter Systeme.- 6.6.3 Definition der Melnikov-Funktion.- 6.7 Verallgemeinerungen des Melnikov-Kriteriums.- 6.7.1 Heterokline Bifurkationen.- 6.7.2 Melnikov-Kriterium für eine Klasse von Hamilton-Systemen mit zwei Freiheitsgraden.- 6.8 Das Shilnikov-Phänomen.- Aufgaben.- 7 Bifurkationen mit höherer Ko-Dimension.- 7.1 Verallgemeinerung der Grundtypen von Bifurkationen eindimensionaler Systeme.- 7.1.1 Eindimensionale Systeme mit kubischen Nichtlinearitäten.- 7.1.2 Eindimensionale Systeme mit quartären Nichtlinearitäten.- 7.2 Die Ko-Dimension dynamischer Systeme.- 7.2.1 Eindimensionale Systeme.- 7.2.2 Ebene Systeme.- 7.2.2.1 Zweidimensionale Potential-Systeme.- 7.2.2.2 Allgemeine zweidimensionale Systeme.- 7.3 Dynamik von Bifurkationen mit Ko-Dimension Zwei.- 7.3.1 Ein doppelter Eigenwert.- 7.3.2 Zwei Paare rein imaginärer Eigenwerte.- Anhang A Versale Entfaltung von Matrizen.- Aufgaben.- Quantitative Methoden der Beschreibung nichtlinearer und chaotischer Systeme.- 8.1 Der (Phasen-)Fluß autonomer Vektorfelder.- 8.2 Nicht-autonome dynamische Systeme.- 8.3 Zur Begriffsbildung bei chaotischen Systemen.- 8.4 Der Lyapunov-Exponent.- 8.4.1 Lyapunov-Exponenten für diskrete, eindimensionale Systeme.- 8.4.2 Lyapunov-Exponenten mehrdimensionaler Systeme.- 8.4.3 Numerische Bestimmung der Lyapunov-Exponenten.- 8.4.4 Lyapunov-Exponenten und Attraktorvolumen.- 8.5 Die Autokorrelationsfunktion.- 8.5.1 Die Autokorrelationsfunktion diskreter Systeme.- 8.5.2 Die Autokorrelationsfunktion kontinuierlicher Systeme.- 8.6 Das Leistungsspektrum.- 8.6.1 Das Leistungsspektrum diskreter Systeme.- 8.6.2 Das Leistungsspektrum kontinuierlicher Systeme.- 8.7 Fraktale Strukturen und Dimensionen.- 8.7.1 Selbstähnlichkeit und Selbstaffinität.- 8.7.2 Fraktale, Hausdorff-Dimension.- 8.7.2.1 Zufallsfraktale.- 8.7.2.2 Multi-Fraktale.- 8.7.3 Selbstähnlichkeits-Dimension.- 8.7.4 Box-Dimension.- 8.7.5 Die informationsdimension.- 8.7.6 Korrelationsdimension.- 8.7.7 Lyapunov-Dimension.- 8.7.8 Die Rényi-Dimension.- 8.7.9 Die Kolmogorov-Entropie.- 8.8 Rekonstruktion eines Attraktors aus einer Zeitreihe.- Aufgaben.- Literatur.- Sachwortverzeichnis.

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Book SynopsisThis volume collects, in written form, eight plenary lectures and twenty-five selected contributions from invited and contributed lectures delivered at the International Workshop on Potential Theory 2004. The workshop was held at Shimane University, Matsue, Japan, from 23 to 28 August, 2004. The topic of the workshop was Potential Theory and its related fields. There were stimulus talks from classical potential theory to pluri-potential theory and probabilistic potential theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

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Book SynopsisBifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.Table of ContentsStructurally Stable Systems; Bifurcations of Dynamical Systems; The Behavior of Dynamical Systems on Stability Boundaries of Equilibrium States; The Behavior of Dynamical Systems on Stability Boundaries of Periodic Trajectories; Local Bifurcations on the Route Over Stability Boundaries; Global Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic Orbits; Bifurcations of Homoclinic Loops of Saddle Equilibrium States; Safe and Dangerous Boundaries.

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Book SynopsisAlthough the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.Table of ContentsIntroduction and basic concepts; nonlinear wave equations in physics; Whitham theory of modulations; complete integrability of nonlinear wave equations; periodic solutions; dissipationless shock wave; nonlinear theory of modulational instability. Appendices: some formulas from the theory of elliptic functions; algebraic resolvents of fourth degree polynomials; solutions to exercises.

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Book SynopsisThis volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.Table of ContentsThe rhomboidal charged four body problem, F. Alfaro and E. Perez-Chavela; planetary rings with shepherds, L. Benet and T.H. Seligman; low Reynolds number swimming in two dimensions, A. Cherman et al; 2-dimensional invariant Tori for the spatial isosceles 3-body problem, M. Corbera and J. Llibre; the global flow for the synodical spatial Kepler problem, M.P. Dantas and J. Llibre; unbounded growth of energy in periodic perturbations of geodesic flows of the torus, A. Delshams et al; splitting and Meinikov potentials in Hamiltonian systems, A. Delshams and P. Gutierrez; infinity manifolds of cubic polynomial Hamiltonian vector fields with 2 degrees of freedom, M. Falconi et al; relativistic corrections to elementary Galilean dynamics and deformations of Poisson brackets, R. Flores-Espinoza and Y.M. Vorobjev; heteroclinic phenomena in the Sitnikov problem, A. Garcia and E. Perez-Chavela); doubly-symmetric periodic solutions of Hill's lunar problem, R.C. Howison and K.R. Meyer; on practical stability regions for the motion of a small particle close to the equilateral points of the real earth-moon system, A. Jorba; variational methods for quasi-periodic solutions of partial differential equations, R. de la Llave; the splitting of invariant Lagrangian submanifolds - geometry and dynamics, J.-P. Marco; cross-sections in the planar N-body problem, C. McCord; existence of an additional first integral and completeness of the flow for Hamiltonian vector fields, J. Mucino-Raymundo; simplification of perturbed Hamiltonians through Lie transformations, J. Palacian and P. Yanguas; linear stability in the 1 + N-Gon relative equilibrium, G.E. Roberts; analytic continuation of circular and elliptic Kepler motion to the general 3-body problem, J. Soler; the phase space of finite systems, K.B. Wolf et al.

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Book SynopsisThis 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.Volume II — shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos, is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phenomena, including life itself.Exclusive Access to the accompanying Video and Audio materials comes with the purchase of this book.

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Book SynopsisThis 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.Volume II — shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos, is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phenomena, including life itself.Exclusive Access to the accompanying Video and Audio materials comes with the purchase of this book.

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Book SynopsisIn recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

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Book SynopsisThe book is devoted to the mathematical foundations of nonextensive statistical mechanics. This is the first book containing the systematic presentation of the mathematical theory and concepts related to nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs statistical mechanics introduced in 1988 by one of the authors and based on a nonadditive entropic functional extending the usual Boltzmann-Gibbs-von Neumann-Shannon entropy. Main mathematical tools like the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects are discussed rigorously with detailed mathematical rational. The book also contains recent results obtained in this direction and challenging open problems. Each chapter is accompanied with additional useful notes including the history of development and related bibliographies for further reading.

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Book SynopsisA recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.

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Book SynopsisThe book is devoted to the problems of modeling physical systems and fields using the tools and capabilities of the 'Mathematica' software package. In the process of teaching classical courses in mechanics and mathematical physics, one often has to overcome significant difficulties associated with the cumbersomeness of the mathematical apparatus, which more than once distracts from the essence of the problems under consideration. The use of the 'Mathematica' package, which has a rich set of analytical and graphic tools, makes the presentation of classic issues related to modeling and interpretation of physical processes much more transparent. This package enables the visualization of both analytical solutions of nonlinear differential equations and solutions obtained in the form of infinite series or special functions.The textbook consists of two parts that can be studied independently of each other. The first part deals with the issues of nonlinear mechanics and the theory of oscillations. The second part covers linear problems of classical mathematical physics and nonlinear evolution models describing, inter alia, transport phenomena and propagation of waves. The book contains the codes of programs written in the 'Mathematica' package environment. Supplementary materials of programs illustrating and often complementing the presented material are available on the publisher's website.

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Book SynopsisIn the early 1980s, the late luminary Tito Arecchi was the first to highlight the existence of chaos in a laser model. Since then, along with several colleagues, he developed many important lines of research in this field, such as generalized multistability, laser with injected signal, laser with delayed feedback and the worldwide accepted classification of lasers of A, B and C, depending on their typical relaxation rates. Later, chaos control and synchronization were investigated in lasers and other systems, providing innovative schemes. Very recently, in his last contribution to laser physics, the model of the laser with feedback demonstrating its universal features was revisited.This book aims to present the research activity of Prof. Arecchi and his colleagues in the domain of nonlinear dynamics of lasers, since his seminal works of 1982 till the latest. Also included is our last contribution on jerk dynamics of laser's minimal universal model and a brief history of the discovery of laser where the reader will discover or rediscover many anecdotes about it.

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Book SynopsisThe topic of nonlinear systems is fundamental to the study of systems engineering. So extensive investigations have been carried out by both the nonlinear control and nonlinear dynamics communities, but the focus can be different — on controllers design and dynamics analysis, respectively. The last two decades have witnessed the gradual merging of control theory and dynamics analysis, but not yet to the extent of controlling nonlinear dynamics such as bifurcations and chaos. This monograph is an attempt to fill that gap while presenting a rather comprehensive coverage of the fundamental nonlinear systems theory in a self-contained and approachable manner.This introductory treatise is written for self-study and, in particular, as an elementary textbook that can be taught in a one-semester course to advanced undergraduates or entrance level graduates with curricula focusing on nonlinear systems, both on control theory and dynamics analysis.

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Book SynopsisOrdinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical systems point of view.This core undergraduate course updated from the dynamical systems perspective can easily be covered in one semester, with room for projects or more advanced topics tailored to the interests of the students.

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Book SynopsisOrdinary differential equations is a standard course in the undergraduate mathematics curriculum that usually comes after the first university calculus and linear algebra courses taken by a mathematics major. Such courses may also typically be attended by undergraduates from other areas of physical and social sciences, and engineering. The content of such a course has remained fairly static over time, despite the expansion of the topic into other disciplines as a result of the dynamical systems point of view.This core undergraduate course updated from the dynamical systems perspective can easily be covered in one semester, with room for projects or more advanced topics tailored to the interests of the students.

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Book SynopsisThe shared platform of the articles collected in this volume is used to advocate a dynamical systems approach to cognition. It is argued that recent developments in cognitive science towards an account of embodiment, together with the general approach of complexity theory and dynamics, have a major impact on behavioral and cognitive science. The book points out that there are two domains that follow naturally from the stance of embodiment: first, coordination dynamics is an established empirical paradigm that is best able to aid the approach; second, the obvious goal-directedness of intelligent action (i.e., intentionality) is nicely addressed in the framework of the dynamical synergetic approach.Table of ContentsIntelligent Behavior - A Synergetic View (H Haken); Cognitive Coordination Dynamics (S Kelso); Grounded in the World: Developmental Origins of the Embodied Mind (Revised Reprint) (E Thelen); What is Coordinated in Bimanual Coordination? (F Mechsner & W Prinz); Cognition in Action: The Interplay of Attention and Bimanual Coordination Dynamics (J J Temprado et a.); A Synergetic Approach to Describe the Stability and Variability of Motor Behaviour (K Witte et al.); The Role of Synchronization in Perception-Action (T-C Chan et al.); A Mean-Field Approach to Self-Organization in Spatially Extended Perception-Action and Psychological Systems (T Frank & P J Beek); Efficiency Aspects of Self-Organizing Systems (W Tschacher et al.); The Embodiment of Intentionality (S Jordan); Cognitive Science, Representations and Dynamical Systems Theory (W F G Haselager); Self-Steered Self-Organization (F Keijzer); SIRN (Synergetic Inter-Representation Networks), Artifacts and Snow's Two Cultures (J Fortugali); Brain Dynamics: Methodological Issues and Applications in Psychiatic and Neurologic Diseases (L Fezard); Dynamical Systems Theory: Applications to Pedagogy (J L Abraham).

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Book SynopsisThis unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

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Book SynopsisThis book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.

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Book SynopsisThis book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.

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Book SynopsisThis elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincare in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing approximate solutions, fails catastrophically due to the problem of small denominators. It then goes on to describe chaotic motion using the tools of discrete maps and Poincare sections. This leads to the two great landmarks of chaos theory, the Poincare-Birkhoff theorem and the so-called KAM theorem, one of the signal results in modern mathematics. The book concludes with an appendix discussing the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics.Lectures on Nonlinear Mechanics and Chaos Theory is written in the easy conversational style of a great teacher. It features numerous computer-drawn figures illustrating the behavior of nonlinear systems. It also contains homework exercises and a selection of more detailed computational projects. The book will be valuable to students and faculty in physics, mathematics, and engineering.See Press Release: Problems in mechanics open the door to the orderly world of chaosTable of ContentsLagrangian Dynamics; Noether's Theorem; Hamiltonian Formulation; Hamilton's Principle Function; Hamilton's Characteristic Function; Action-Angle Variables; Abstract Transformation Theory; Poisson Brackets; Liouville's Theorem; Perturbation Theory; The Henon-Heiles Oscillator; Discrete Maps; Lyapunov Exponents; The Poincare-Birkhoff Theorem; The KAM Theorem; Ergodic Hypothesis; Measure Theory;

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Book SynopsisThis elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincare in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing approximate solutions, fails catastrophically due to the problem of small denominators. It then goes on to describe chaotic motion using the tools of discrete maps and Poincare sections. This leads to the two great landmarks of chaos theory, the Poincare-Birkhoff theorem and the so-called KAM theorem, one of the signal results in modern mathematics. The book concludes with an appendix discussing the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics.Lectures on Nonlinear Mechanics and Chaos Theory is written in the easy conversational style of a great teacher. It features numerous computer-drawn figures illustrating the behavior of nonlinear systems. It also contains homework exercises and a selection of more detailed computational projects. The book will be valuable to students and faculty in physics, mathematics, and engineering.See Press Release: Problems in mechanics open the door to the orderly world of chaosTable of ContentsLagrangian Dynamics; Noether's Theorem; Hamiltonian Formulation; Hamilton's Principle Function; Hamilton's Characteristic Function; Action-Angle Variables; Abstract Transformation Theory; Poisson Brackets; Liouville's Theorem; Perturbation Theory; The Henon-Heiles Oscillator; Discrete Maps; Lyapunov Exponents; The Poincare-Birkhoff Theorem; The KAM Theorem; Ergodic Hypothesis; Measure Theory;

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Book SynopsisThe main goal is to offer to readers a panorama of recent progress in nonlinear physics, complexity and transport with attractive chapters readable by a broad audience. It allows to gain an insight into these active fields of research and notably promotes the interdisciplinary studies from mathematics to experimental physics. To reach this aim, the book collects a selection of contributions to the third edition of the CCT conference (Marseilles, 1-5 June 2015).

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Book SynopsisOur book presents a unique and original viewpoint on natural and engineered systems. The authors' goal is to propose and explain core principles that govern the formation and function of simple and complex systems. Examples are drawn from a broad range of topics from common materials and manufactured structures to the behavior of cells, organisms and socio-economic organizations. We provide a technical discussion of key engineering principles without the use of mathematics so that we may describe for a general audience how the systems of daily life form, operate, and evolve. We use analogy and illustrations to show how the components self-organize and scale to form complex adaptive systems. In this way we hope to understand how those systems come to be, achieve stability, and suddenly transition to new equilibrium states, including the sudden onset of economic recessions, ecosystem collapse, the evolution of species, development of cancer, and other wide-ranging topics. The existential role of component variability in these processes is emphasized.This book targets engineering instructors and undergraduate students curious to explore the grand challenges facing society today so they might build productive and long-lasting careers in science and technology. The six essays can be used to frame classroom discussions on systems from a broad range of disciplines. The essays are designed to appeal to those with a basic science and engineering background as we illustrate many fundamental engineering concepts in our descriptions of system behavior. We also hope our book appeals to curious members of the general public who are interested in understanding foundational ideas.

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Book SynopsisOur book presents a unique and original viewpoint on natural and engineered systems. The authors' goal is to propose and explain core principles that govern the formation and function of simple and complex systems. Examples are drawn from a broad range of topics from common materials and manufactured structures to the behavior of cells, organisms and socio-economic organizations. We provide a technical discussion of key engineering principles without the use of mathematics so that we may describe for a general audience how the systems of daily life form, operate, and evolve. We use analogy and illustrations to show how the components self-organize and scale to form complex adaptive systems. In this way we hope to understand how those systems come to be, achieve stability, and suddenly transition to new equilibrium states, including the sudden onset of economic recessions, ecosystem collapse, the evolution of species, development of cancer, and other wide-ranging topics. The existential role of component variability in these processes is emphasized.This book targets engineering instructors and undergraduate students curious to explore the grand challenges facing society today so they might build productive and long-lasting careers in science and technology. The six essays can be used to frame classroom discussions on systems from a broad range of disciplines. The essays are designed to appeal to those with a basic science and engineering background as we illustrate many fundamental engineering concepts in our descriptions of system behavior. We also hope our book appeals to curious members of the general public who are interested in understanding foundational ideas.

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