Contents - ChaosBook

ContentsPart I: Classical chaosContributors ................................Acknowledgements ............................iiivi1 Overture 11.1 Why ChaosBook? .......................... 21.2 Chaos ahead ............................. 31.3 The future as in a mirror ...................... 41.4 A game of pinball .......................... 91.5 Chaos for cyclists .......................... 131.6 Evolution .............................. 191.7 To statistical mechanics ....................... 211.8 What is not in ChaosBook ..................... 22résumé 23 commentary 25 guide to exercises 28 exercises 29 references 292 Go with the flow 322.1 Dynamical systems ......................... 322.2 Flows ................................ 362.3 Computing trajectories ....................... 40résumé 41 commentary 41 exercises 43 references 443 Discrete time dynamics 463.1 Poincaré sections .......................... 463.2 Constructing a Poincaré section ................... 533.3 Maps ................................ 54résumé 57 commentary 57 exercises 59 references 594 Local stability 614.1 Flows transport neighborhoods ................... 614.2 Linear flows ............................. 654.3 Stability of flows .......................... 714.4 Neighborhood volume ....................... 754.5 Stability of maps .......................... 77résumé 79 commentary 80 exercises 81 references 825 Cycle stability 835.1 Stability of periodic orbits ..................... 835.2 Cycle Floquet multipliers are cycle invariants ........... 87ii