Bøger i Institute for Nonlinear Scienc serien

A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.

This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes. Specific discussions include:¿ Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior.¿ Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems.¿ Random matrix theory and supersymmetry. The book is divided into several parts. Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems. Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques. Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively. Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapter 9 discusses the quantum mechanics of systems driven by time-periodic forces. Chapter 10 reviews some recent work on the stochastic manifestations of chaos.The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature. End of chapter problems help students clarify their understanding. In this new edition, the presentation has been brought up to date throughout, and a new chapter on open quantum systems has been added.About the author:Linda E. Reichl, Ph.D., is a Professor of Physics at the University of Texas at Austin and has served as Acting Director of the Ilya Prigogine Center for Statistical Mechanics and Complex Systems since 1974. She is a Fellow of the American Physical Society and currently is U.S. Editor ofthe journal Chaos, Solitons, and Fractals.