Description
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.
