Deterministic Chaos – An Introduction 4e

Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. In 1971 he attained his doctorate and in 1976 he was appointed Professor at the University of Frankfurt am Main in Germany. He was a visiting professor at the Weizmann--Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. Wolfram Just is Lecturer for Applied Mathematics at Queen Mary/University of London. He held positions at different institutions, for instance Kyushu University Fukuoka/Japan, MPIPKS Dresden/Germany, and Chemnitz University of Technology/Germany. His current research interests are nonlinear dynamics of systems with many degrees of freedom and nonequilibrium statistical physics.

Preface. Color Plates. 1 Introduction. 2 Experiments and Simple Models. 2.1 Experimental Detection of Deterministic Chaos. 2.2 The Periodically Kicked Rotator. 3 Piecewise Linear Maps and Deterministic Chaos. 3.1 The Bernoulli Shift. 3.2 Characterization of Chaotic Motion. 3.3 Deterministic Diffusion. 4 Universal Behavior of Quadratic Maps. 4.1 Parameter Dependence of the Iterates. 4.2 Pitchfork Bifurcation and the Doubling Transformation. 4.3 Self--Similarity, Universal Power Spectrum, and the Influence of External Noise. 4.4 Behavior of the Logistic Map for r & r. 4.5 Parallels between Period Doubling and Phase Transitions. 4.6 Experimental Support for the Bifurcation Route. 5 The Intermittency Route to Chaos. 5.1 Mechanisms for Intermittency. 5.2 Renormalization--Group Treatment of Intermittency. 5.3 Intermittency and 1/f--Noise. 5.4 Experimental Observation of the Intermittency Route. 6 Strange Attractors in Dissipative Dynamical Systems. 6.1 Introduction and Definition of Strange Attractors. 6.2 The Kolmogorov Entropy. 6.3 Characterization of the Attractor by a Measured Signal. 6.4 Pictures of Strange Attractors and Fractal Boundaries. 7 The Transition from Quasiperiodicity to Chaos. 7.1 Strange Attractors and the Onset of Turbulence. 7.2 Universal Properties of the Transition from Quasiperiodicity to Chaos. 7.3 Experiments and Circle Maps. 7.4 Routes to Chaos. 8 Regular and Irregular Motion in Conservative Systems. 8.1 Coexistence of Regular and Irregular Motion. 8.2 Strongly Irregular Motion and Ergodicity. 9 Chaos in Quantum Systems? 9.1 The Quantum Cat Map. 9.2 A Quantum Particle in a Stadium. 9.3 The Kicked Quantum Rotator. 10 Controlling Chaos. 10.1 Stabilization of Unstable Orbits. 10.2 The OGY Method. 10.3 Time--Delayed Feedback Control. 10.4 Parametric Resonance from Unstable Periodic Orbits. 11 Synchronization of Chaotic Systems. 11.1 Identical Systems with Symmetric Coupling. 11.2 Master--Slave Configurations. 11.3 Generalized Synchronization. 11.4 Phase Synchronization of Chaotic Systems. 12 Spatiotemporal Chaos. 12.1 Models for Space--Time Chaos. 12.2 Characterization of Space--Time Chaos. 12.3 Nonlinear Nonequilibrium Space--Time Dynamics. Outlook. Appendix. A Derivation of the Lorenz Model. B Stability Analysis and the Onset of Convection and Turbulence in the Lorenz Model. C The Schwarzian Derivative. D Renormalization of the One--Dimensional Ising Model. E Decimation and Path Integrals for External Noise. F Shannon's Measure of Information. F.1 Information Capacity of a Store. F.2 Information Gain. G Period Doubling for the Conservative H-enon Map. H Unstable Periodic Orbits. Remarks and References. Index.