Chaos - Classical and Quantum - P. Civitanovic.pdf

Chaos: Classical and
Quantum
Part I: Deterministic Chaos
Predrag Cvitanovi´c – Roberto Artuso – Ronnie Mainieri – Gregor
Tanner – G´abor Vattay – Niall Whelan – Andreas Wirzba
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/, Aug 30 2006 printed August 30, 2006
comments to: ******@
ii
Contents
Part I: Classical chaos
Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
1 Overture 1
Why ChaosBook? . . . . . . . . . . . . . . . . . . . . . . . . 2
Chaos ahead . . . . . . . . . . . . . . . . . . . . . . . . . . 3
The future as in a mirror . . . . . . . . . . . . . . . . . . . 4
A game of pinball . . . . . . . . . . . . . . . . . . . . . . . . 9
Chaos for cyclists . . . . . . . . . . . . . . . . . . . . . . . . 14
Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
From chaos to statistical mechanics . . . . . . . . . . . . . . 22
A guide to the literature . . . . . . . . . . . . . . . . . . . . 23
guide to exercises 26 - resum´e27 - references 28 - exercises 30
2 Go with the flow 31
Dynamical systems . . . . . . . . . . . . . . . . . . . . . . . 31
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
trajectories . . . . . . . . . . . . . . . . . . . . . 39
resum´e40 - references 40 - exercises 42
3 Do it again 45
Poincar´esections . . . . . . . . . . . . . . . . . . . . . . . . 45
Constructing a Poincar´esection . . . . . . . . . . . . . . . . 48
Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
resum´e53 - references 53 - exercises 55
4 Local stability 57
Flows transport neighborhoods . . . . . . . . . . . . . . . . 57
Linear flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Stability of flows . . . . . . . . . . . . . . . . . . . . . . . . 64
Stability of maps . . . . . . . . . .