Chaos theory Books

Book SynopsisWhat is time? The Janus Point offers a ground-breaking solution to one of the greatest mysteries in physics.For over a century, the greatest minds have sought to understand why time seems to flow in one direction, ever forward. In The Janus Point, Julian Barbour offers a radically new answer: it doesn't.At the heart of this book, Barbour provides a new vision of the Big Bang - the Janus Point - from which time flows in two directions, its currents driven by the expansion of the universe and the growth of order in the galaxies, planets and life itself. What emerges is not just a revolutionary new theory of time, but a hopeful argument about the destiny of our universe.'Both a work of literature and a masterpiece of scientific thought' Lee Smolin, author of The Trouble with Physics'Profound...original...accessible to anyone who has pondered the mysteries of space and time' Martin Rees, Astronomer Royal 'Takes on fundamental questions, offering a new perspective on how the Universe started and where it may be headed' Science MagazineTrade ReviewJulian Barbour is a profound and original thinker with the boldness to tackle some of nature's deepest problems. He is also a fine writer, and this renders his book - despite its conceptual depth - accessible to anyone who has pondered the mysteries of space and time -- Martin Rees, Astronomer Royal and former President of the Royal SocietyWith a rare humanity and a perspective based on a lifetime of study, Barbour writes a book that is both a work of literature and a masterpiece of scientific thought -- Lee Smolin, author of The Trouble with PhysicsThe origin of the arrow of time is arguably the most important conceptual problem in cosmology, and the prospect that it can be solved in a universe where time flows "backward" in the far past is as exciting as it is provocative. In this engaging book, Julian Barbour conveys this excitement admirably -- Sean Carroll, author of From Eternity to HereThe Janus Point shows history-in-the-making: a project to recast the foundations of all of cosmology, gravity, thermodynamics and the arrow of time. The book has given me a lot to ponder. As Gauss said of Riemann's habilitation lecture, '[it] exceeded my expectations' -- Bill Unruh, Professor of Physics at University of British ColumbiaJulian Barbour has no peer when it comes to explaining scientific ideas in a way that is accessible without being simplistic -- Neal Stephenson, author of Snow CrashJulian Barbour has discovered an unexpected and remarkably simple feature of Newtonian dynamics that is the basis of his seductive and eloquently presented explanation of the history of the universe, even time itself -- Michael Victor Berry, Professor of Physics (Emeritus) at Bristol UniversityThis delightful, provocative book is a cosmic physics adventure, enlivened with history and poetry -- Theodore A. Jacobson, Professor of Physics at University of MarylandJulian Barbour has a complete mastery of the history of ideas yet a remarkable lightness and clarity in explaining what are profound concepts. The Janus Point is controversial and gripping, an extraordinary introduction to his view of the universe -- Pedro G. Ferreira, author of The Perfect TheoryBarbour takes on fundamental questions, offering a new perspective - illustrated with lucid examples and poetically constructed prose - on how the Universe started (or more precisely, how it did not start) and where it may be headed. This book is an engaging read, which both taught me something new about meat-and-potatoes physics and reminded me why asking fundamental questions can be so fun -- Matthew Johnson * Science *A closely argued, substantive take on one of the biggest unsolved mysteries of physics, written by someone who has wrestled with not only the physics, but also the history and philosophy relevant to his subject. What's more, Barbour's approach, unlike many in the popular science game, is to publish only when he thinks he has something worth saying. That alone is enough to make him worth listening to -- Michael Brooks * Nautilus *Julian Barbour is one that rare breed, an optimistic scientist, and his engrossing The Janus Point not only turns accepted thinking about the universe on its head...but also suggests our very understanding of the nature of time needs to be reappraised * Choice *Any reader willing to engage with Barbour's ideas will come away enlightened -- Sidney Perkowitz * Physics World *

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Book SynopsisUncover one of the most exciting frontiers of modern physics in this fascinating, insightful and accessible overview of Chaos theory.An exceedingly readable introduction to a new intellectual world' ObserverFrom the turbulence of the weather to the complicated rythmns of the human heart, chaos' is at the centre of our day to day lives. Cutting across several scientific disciplines, James Gleick explores and elucidates the science of the unpredicatable with an immensely readable narrative style and flair.An awe-inspiring book. Reading Chaos gave me the sensation that someone had just found the light-switch' Douglas AdamsTrade ReviewFascinating... Almost every paragraph contains a jolt * New York Times *Highly entertaining...a startling look at newly discovered universal laws * Chicago Tribune *

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Book SynopsisNATIONAL BESTSELLER • From the classroom to the courtroom and from financial markets to supermarkets, an intriguing and illuminating look at how randomness, chance, and probability affect our daily lives that will intrigue, awe, and inspire.“Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists.... The result is a readable crash course in randomness.” —The New York Times Book ReviewWith the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more

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Book SynopsisBuilding on her bestseller, The Intention Experiment, Lynne McTaggart’s groundbreaking work The Bond reveals the latest science to prove that we are all connected, that collaboration trumps competition, and that empathy is essential—now in paperback.A BOLD NEW VISION FOR A NEW WORLD Our way of life isn’t working anymore. People are losing their jobs, their homes, their neighborhoods—and even their hope for a just society. We urgently need a new story to live by, based on fairness—not simply on the accumulation of wealth and “survival of the fittest.” The Bond offers a radical new blueprint for living a more harmonious, prosperous, and connected life. International bestselling author Lynne McTaggart demonstrates with hard science that we are living contrary to our true nature. In fact, life doesn’t have to be I win, you lose; we have been designed to succeed and pros

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Book SynopsisThe million-copy New York Times bestseller and finalist for both the Pulitzer Prize and the National Book Award that reveals the science behind chaos theoryA work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking bestseller Chaos introduces a whole new readership to chaos theory, one of the most significant waves of scientific knowledge in our time. From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

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Book SynopsisIn the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman''s fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produTrade Review'provides an enjoyable and clearly written introduction to the structure and properties of Poisson processes ... Thanks to skillful steering away from, and around, technicalities, it is widely accessible. If you don't know the story, read this book - you will then know what you are missing. If you do know it, a browse through the book, particularly the later chapters, is still worthwhile for interesting perspectives on several areas.' P.J. Donnelly, Queen Mary and Westfield College, Short Book Reviews (Publication of the International Statistical Institute)'It records the author's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions.' L'Enseignement Mathématique, 3-4, 1993'Every mathematician with some knowledge of stochastic processes is aware of the interest and importance of the Poisson process. Therefore it is very useful to have now a book which is devoted to a systematic treatment of Poisson processes. The book ... fulfills the expectations one might have when a famous elder author writes a book on a classic topic. It gives the basic facts in a clear and lucid way. It is shown how the theory can be applied to interesting problems of astronomy, queueing and traffic, etc., and these examples are studied very thoroughly and deeply, giving even the specialist new insights ... an excellent basis for lectures or seminars .... a valuable gift for a young mathematician to stimulate his or her interest in stochastic processes and in applied probability in general.' Mathematical Reviews, Issue 94a'The presentation everywhere is rigorous without being fuzzy about measure theoretical details; this would make the monograph suitable for many readrs, who are either not interested or not trained in measure theoretical subtleties ... a useful addition to the literature both for various beginners as well as for lecturers in the theory of stochastic processes who would find in it a rich array of topics presented clearly.' S.D. Chatterji, Mathematics Abstracts, 773/93The Poisson process is surely the most beautiful object in probability theory, and John Kingman is its most gifted expositor. One might have been forgiven for thinking that there would be little new to say, but in fact this book is studded with new and fascinating insights. It is rare to find a book that simultaneously addresses the beginner and the expert. If there were a prize for the wisest probability book of the decade it would have to go to Bristol's Vice-Chancellor. * David Kendall, Cambridge, Journal of Royal Statistical Society, 1994 *Table of ContentsStochastic models for random sets of points; Poisson processes in general spaces; Sums over Poisson processes; Poisson processes on the line; Marked Poisson processes; Cox processes; Stochastic geometry; Complete random measures; The Poisson-Dirichlet distribution.

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Book SynopsisThis is an advanced textbook on the subject of turbulence, and is suitable for engineers, physical scientists and applied mathematicians. The aim of the book is to bridge the gap between the elementary accounts of turbulence found in undergraduate texts, and the more rigorous monographs on the subject. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. Chapters 1 to 5 may be appropriate as background material for an advanced undergraduate or introductory postgraduate course on turbulence, while chapters 6 to 10 may be suitable as background material for an advanced postgraduate course on turbulence, or act as a reference source for professional researchers.This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the EarthTable of ContentsTHE CLASSICAL PICTURE OF TURBULENCE; FREELY-DECAYING, HOMOGENEOUS TURBULENCE; SPECIAL TOPICS

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Book SynopsisUsing the explosion in the use of chaos theory, this book examines the relationship between science and other disciplines as well as the place of scientific knowledge within our broader culture.Trade Review"Over the next several decades, we will continue to see the issues raised in Borrowed Knowledge and the Challenge of Learning across Disciplines as important to understanding both the natural and human sciences." - Douglas Kiel, University of Texas at Dallas"

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Book SynopsisOne of the most striking applications of chaos theory in recent years, non-linear pricing uses genetic algorithms, fuzzy logic, fractal imaging and other cutting-edge technologies to identify and exploit patterns hidden within the seemingly helter-skelter rise and fall of daily stock prices.Trade Review"A lively and intriguing book from a writer who can range from Zen to mathematics."-Adam Smith, author of The Money Game and Paper Money "Nonlinear Pricing is an eminently readable book which I found satisfied both the theorist and the practitioner in me. For the theorist, there are new insights into the relationship between complexity and the markets. For the practitioner, there are practical ideas on how to fashion investment strategies. I highly recommend Nonlinear Pricing to all students of the markets."-Edgar E. Peters, Chief Investment Strategist, PanAgora Asset Management; author, Chaos and Order in the Capital Markets "Nonlinear Pricing goes further than any book I am aware of in drawing a connection between the real world of economics and the new ideas about economics coming from the science of self-organized systems. Written in a lively, informal style, this is a wonderful read for those of us who have been wondering whether anyone understands anything at all about how markets work."-Lee Smolin, PhD, Department of Physics, Pennsylvania State University "Required reading for the enlightened financial professional. Enjoyable for the intelligent investor. A dash of physics, bite-sized pieces of nonlinear concepts, and a broth of hands-on experience make this a cookbook for the modern trader."-Richard E. Morley, Potts Medal recipient and founder of the Breakfast Club "A real eye-opener-Nonlinear Pricing explains a complex subject in easy terms and makes the reader aware of the many opportunities offered by this new technology." -Richard Olsen, founder, Olsen and Associates, Zurich "I, of course, think highly of this book as it credits Dance of the Money Bees with inventing 'swarm theory', now a discipline in computer science. There are many other splendid insights." -John Train, author and President of the Montrose Fund "An extraordinary tour d'horizon, this book challenges conventional thinking about finance, investing, and much else besides. Brimming with ideas and eye-opening connections, it makes a powerful case for our need to understand the extent to which nonlinearity shapes our lives." -Andrew Freeman, Managing Editor, Financial Services, The Economist Intelligence Unit; co-author, Seeing Tomorrow: Rewriting the Rules of Risk "Nonlinear Pricing: Theory & Application by Christopher T. May makes nice reading even for people like me who are not economists. This is an ambitious book as it presents economics starting from fundamental physics. It deserves a large readership." -Ilya Prigogine, 1977 Nobel Laureate, Chemistry; author, The End of Certainty; and the world's foremost non-equilibrium scientistTable of ContentsA Toy Story for Wall Street. Nonlinearity: A Retrospective. Nonlinearity: A Prospective. Fractal Analysis. Results of the Hurst Exponent. Nonlinear Technology. Biology and the S&P. Father Time. Nonlinear Pricing-Advanced Concepts. The Last Word-Resonance. Appendix. Glossary. Bibliography. Index.

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Book SynopsisA powerful new way to navigate today's unprecedented market conditions "Bill Williams' pioneering application of chaos theory to the financial markets is leading technical analysis into the twenty-first century and beyond.Table of ContentsBlasting Off. From Chaos to Cosmos to Cash. The Alligator. The Fractal-The Breakaway Trade. The Awesome Oscillator. The Market Accelerator. Trading in the Zones. The Balance Line Trades. Techniques for Taking Profits. Tying It All Together. How to Become a Master Trader. Bibliography. About the Author. Index.

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Book SynopsisA leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena.Table of ContentsFRACTAL TIME SERIES. Failure of the Gaussian Hypothesis. A Fractal Market Hypothesis. FRACTAL (R/S) ANALYSIS. Measuring Memory--The Hurst Process and R/S Analysis. Testing R/S Analysis. Finding Cycles: Periodic and Nonperiodic. APPLYING FRACTAL ANALYSIS. Case Study Methodology. Dow Jones Industrials, 1888-1990: An Ideal Data Set. S&P 500 Tick Data, 1989-1992: Problems with Oversampling. Volatility: A Study in Antipersistence. Problems with Undersampling: Gold and U.K. Inflation. Currencies: A True Hurst Process. FRACTAL NOISE. Fractional Noise and R/S Analysis. Fractal Statistics. Applying Fractal Statistics. NOISY CHAOS. Noisy Chaos and R/S Analysis. Fractal Statistics, Noisy Chaos, and the FMH. Understanding Markets. Appendices. Bibliography. Glossary. Index.

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Book SynopsisWhat is life? Is it just the biologically familiar - birds, trees, snails, people - or is it an infinitely complex set of patterns that a computer could simulate? This book outlines many of the challenges and controversies involved in the dynamic and curious science of artificial life.Trade Review"Emmeche's account goes beyond describing (with appropriate awe) the accomplishments of computer biology to raise the crucial question of whether the new metaphor of the machine can be extended ... to the whole of nature."--Times Literary Supplement "A serious, sensible introduction to an exciting new field. It is not every day that one can see science fiction clash with natural philosophy in such a civilized fashion."--Karl Sigmund, Science "Can life be synthesized? Emmeche suggests in his fascinating book an approach to this question by means of computer simulation of living processes ... [and] tackles the posed questions with great insight."--Borje Ekstig, The Quarterly Review of BiologyTable of ContentsPrefaceAcknowledgementsCh. 1The Game of Life3Ch. 2What Is Life?23Ch. 3The Logic of Self-Reproduction47Ch. 4Artificial Growth and Evolution71Ch. 5The Ecology of Computation110Ch. 6The Biology of the Impossible134Ch. 7Simulating Life: Postmodern Science156Notes167Index189

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Book SynopsisIntroduces readers to advances in American space exploration. This book discusses ways to capture and redirect asteroids; presents research on the origin of the Moon; weighs in on discoveries like 2003 UB313, a dwarf planet detected in the far outer reaches of our solar system - and, more.Trade Review"[This book] will truly excite anyone interested in the future of space travel... Grounded in real physics, Belbruno's ideas will tantalize the space audience."--Gilbert Taylor, Booklist "A small group of scientists has worked on new orbits that take into account the inherently chaotic motion of object in a multibody system... One of the innovators in what is known as 'capture dynamics', Ed Belbruno, provides a basic and eminently readable introduction to the topic in Fly Me to the Moon."--Jeff Foust, The Space Review "This book does for mathematics what The Double Helix did for biochemistry, without the gossip and diatribe that made The Double Helix so controversial...Overall, this book is a superb introduction to the life of a real mathematician, and a gentle introduction to some very complex mathematics."--Jeff Suzuki, MAA Review "Fly Me to the Moon provides a fast, very readable account of new developments in chaotic celestial mechanics, especially low-fuel space travel, at a level appropriate for a general audience. By the end, nonmathematicians will have gained some intuition about one of the hallmarks of chaos, sensitive dependence on initial conditions, and how chaos can be harnessed to good purpose. All readers will walk away thinking differently about the cosmos. Far from being a clockwork, it will seem more dynamic, more turbulent, and full of diverse possibilities."--Shane Ross, Notices of the American Mathematical Society "Belbruno beautifully describes his novel low-fuel concept in Fly Me to the Moon, using copious sketches to explain his theory without resorting to a single equation... The author has laid out the book very well--a teaser of an introduction with just enough details of the Hiten rescue to whet the appetite, but leaving you hungry for more. The language is friendly yet enticing, with nice snappy chapter lengths and informative illustrations in just the right places. There is a good story line running through the book with little surprises like the author being granted a patent for his special route to the Moon in 2003, with many more patents to follow for routes to other destinations."--Gerard McMahon, Astronomy and Space "[A] wonderfully informative book... For anyone with an interest in this remarkable development in spaceflight the book is a must."--Colin Keay, Australian PhysicsTable of ContentsForeword by Neil deGrasse Tyson ix Preface xiii Acknowledgments xvii Chapter 1 A Moment of Discovery 1 Chapter 2 An Uncertain Start 5 Chapter 3 Conventional Way to the Moon 9 A Fuel Hog 14 Chapter 4 A Question 17 Chapter 5 Chaos and Surfing the Gravitational Field 29 What Is Chaos? 31 Chapter 6 Using Art to Find Chaotic Regions 37 An Oil Painting Unveiling Dynamical Processes 37 Chapter 7 WSB--A Chaotic No-Man's-Land 41 Chapter 8 Getting to the WSB--Low Energy Transfers 49 Chapter 9 Rescue of a Lunar Mission 55 Skepticism, Politics, and a Bittersweet Success 63 Chapter 10 Significance of Hiten 69 Chapter 11 Salvage of HGS-1, and a Christmas Present 77 Chapter 12 Other Space Missions and Low Energy Transfers 83 LGAS Reincarnated: SMART 1 83 Europa Orbiter and Prometheus 85 A Lunar Transportation System 91 Chapter 13 Hopping Comets and Earth Collision 95 Potential Earth Collision 108 Lexell 109 Jupiter-Hopping Earth-Crossing Comets Present a Danger 111 Kuiper Belt Objects and Neptune Hopping 113 Ballistic Escape from the Earth-Moon System, and Asteroid Capture 115 Chapter 14 The Creation of the Moon by Another World 119 Chapter 15 Beyond the Moon and to the Stars 129 Pluto to Alpha Centauri 129 Comets Moving between the Sun and Alpha Centauri 133 Chapter 16 A Paradigm Shift and the Future 137 Bibliography 141 Index 147

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Book SynopsisThe author presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.Trade Review"Feldman succeeds in introducing the reader to the world of dynamic systems and the, almost mythical, chaos that they can produce."---Adhemar Bultheel, European Mathematical Society"[A] gentle and loving introduction to dynamical systems. . . . Chaos and Dynamical Systems is a book for everyone from the layman to the expert."---David S. Mazel, MAA Reviews

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Book SynopsisSymmetry suggests order and regularity whilst chaos suggests disorder and randomness. Symmetry in Chaos is an exploration of how combining the seemingly contradictory symmetry and chaos can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics, and between symmetry and chaos. The underlying mathematics involved in the generation of the images is described. This second edition has been updated to include the Faraday experiment, a classical experiment from fluid dynamics which illustrates that increasing the vibration amplitude of a container of liquid causes the liquid to form surface waves, instead of moving as a solid body. This second edition also includes updated methods for numerically determining the symmetry of higher dimensional analogues of the images. As well as this, it contains new and improved quality images.

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Book SynopsisA First Course in Chaotic Dynamical Systems: Theory and Experiment, Second EditionThe long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to sTable of ContentsPreface to the Second Edition, 1. A Visual and Historical Tour, 2. Examples of Dynamical Systems, 3. Orbits, 4. Graphical Analysis, 5. Fixed and Periodic Points, 6. Bifurcations, 7. The Quadratic Family, 8. Transition to Chaos, 9. Symbolic Dynamics, 10. Chaos, 11. Sharkovsky’s Theorem, 12. Role of the Critical Point, 13. Newton’s Method, 14. Fractals, 15. Complex Functions, 16. The Julia Set, 17. The Mandelbrot Set, 18. Other Complex Dynamical Systems, Appendices, Bibliography, Index

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Book SynopsisLiterature and Ecotheology: From Chaos to Cosmos challenges us in a time of climate crisis to find more common ground between the dual projects of ecocriticism and ecotheology.This book argues that in our postsecular age, literature has become an important repository of theological wisdom that can, like formal work in ecotheology, provide the moral grounds for environmental care. However, for any cosmological understanding to be adequate to the challenges before us, it must be responsive to the often-painful contingencies and uncertainties that inhere in the cosmos, something that both ecocriticism and ecotheology have often neglected. After a treatment of the ecocritical and ecotheological questions that pertain to the religious/secular divide, the study then turns to four contemporary American writersAnnie Dillard, Cormac McCarthy, Marilynne Robinson, and David James Duncanas examples. Each uses the contingency of literary form and its promise of wholeness in order t

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Book SynopsisThe theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.Table of ContentsPreface; 1. Introduction; 2. Linear cocycles; 3. Extremal Lyapunov exponents; 4. Multiplicative ergodic theorem; 5. Stationary measures; 6. Exponents and invariant measures; 7. Invariance principle; 8. Simplicity; 9. Generic cocycles; 10. Continuity; References; Index.

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Book SynopsisThe editors (of the Universite et Institut National des Sciences Appliquees de Rouen, France) present six chapters exploring the application of chaos theory to such topics as the topological characterisation of attractors and the reconstruction of equations of motion from data. Specific topics include the development of a method of modelling called NARMAX (non-linear autoregressive moving average models with exogenous outputs), a summary of the work of the Centre of Applied Dynamics and Optimisation at the U. of Western Australia), time delayed feedback systems, and global modelling applications to biological data and secure communication.

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Book SynopsisThis book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

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Book SynopsisThis self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet's Linear and Nonlinear Functional Analysis with Applications (SIAM), where the titular topics were not treated. Pedagogical features such as detailed theorems and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study.The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

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Book SynopsisThe Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication.The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural.These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.

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Book SynopsisThis important book presents the most important articles by leading scholars in their fields which bring together three basic aspects of research into nonlinear dynamics and economics. The first papers deal with the theoretical methods used in analysing chaotic dynamics and the statistical tools to detect the presence of non linearities in economic data. The following articles discuss the models which are currently being used to stimulate nonlinear economic phenomena. The final papers apply these methods to a number of economic time series.The editor has written a new introduction to accompany the piece.Table of ContentsContents: Acknowledgements Introduction Part I: Methods Part II: Models Part III: Evidence Index

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Book Synopsis2024 Nautilus Book Award Winner * The Marginalian Favorite Books of 2023An electrifying introduction to complexity theory, the science of how complex systems behave, that explains the interconnectedness of all things and that Deepak Chopra says, “will change the way you understand yourself and the universe.”Nothing in the universe is more complex than life. Throughout the skies, in oceans, and across lands, life is endlessly on the move. In its myriad forms—from cells to human beings, social structures, and ecosystems—life is open-ended, evolving, unpredictable, yet adaptive and self-sustaining. Complexity theory addresses the mysteries that animate science, philosophy, and metaphysics: how this teeming array of existence, from the infinitesimal to the infinite, is in fact a seamless living whole and what our place, as conscious beings, is within it.The implications of complexity theory are profound, providing insight into everything from the permeable boundaries of our bodies to the nature of consciousness. Notes on Complexity is an invitation to trade our limited, individualistic view for the expansive perspective of a universe that is dynamic, cohesive, and alive—a whole greater than the sum of its parts. Physician, scientist, and philosopher Neil Theise takes us to the exhilarating frontiers of human knowledge and in the process restores wonder and meaning to our experience of the everyday.

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Book Synopsis2024 Nautilus Book Award Winner * The Marginalian Favorite Books of 2023An electrifying introduction to complexity theory, the science of how complex systems behave, that explains the interconnectedness of all things and that Deepak Chopra says, “will change the way you understand yourself and the universe.”Nothing in the universe is more complex than life. Throughout the skies, in oceans, and across lands, life is endlessly on the move. In its myriad forms—from cells to human beings, social structures, and ecosystems—life is open-ended, evolving, unpredictable, yet adaptive and self-sustaining. Complexity theory addresses the mysteries that animate science, philosophy, and metaphysics: how this teeming array of existence, from the infinitesimal to the infinite, is in fact a seamless living whole and what our place, as conscious beings, is within it.The implications of complexity theory are profound, providing insight

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Book SynopsisThis book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.Table of ContentsForeword.- Preliminaries on Advanced Calculus.- Hamiltonian Systems Theory.- Normal Forms of Hamiltonian Systems.- Spectral Decomposition of Hamiltonian Matrices.- The General Linear Normalization.- Stability of Equilibria.- Stability of Linear Hamiltonian Systems.- Parametric Resonance.- References.- 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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