Chaos: Classical and
Quantum
Part I: DeterministicChaos
Predrag Cvitanović – Roberto Artuso – Ronnie Mainieri – Gregor
Tanner – Gábor Vattay – Niall Whelan – Andreas Wirzba
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ChaosBook.org/version11.8, Aug 30 2006
printed August 30, 2006
ChaosBook.org
comments to: predrag@nbi.dk
ii
Contents
Part I: Classical chaos
Contributors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
1 Overture
1
1.1 Why ChaosBook? . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2 Chaos ahead
. . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.3 The future as in a mirror
. . . . . . . . . . . . . . . . . . .
4
1.4 A game of pinball . . . . . . . . . . . . . . . . . . . . . . . .
9
1.5 Chaos for cyclists . . . . . . . . . . . . . . . . . . . . . . . .
14
1.6 Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1.7 From chaos to statistical mechanics . . . . . . . . . . . . . .
22
1.8 A guide to the literature . . . . . . . . . . . . . . . . . . . .
23
guide to exercises 26 - resumé 27 - references 28 - exercises 30
2 Go with the flow
31
2.1 Dynamical systems . . . . . . . . . . . . . . . . . . . . . . .
31
2.2 Flows
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.3 Computing trajectories . . . . . . . . . . . . . . . . . . . . .
39
resumé 40 - references 40 - exercises 42
3 Do it again
45
3.1 Poincaré sections . . . . . . . . . . . . . . . . . . . . . . . .
45
3.2 Constructing a Poincaré section . . . . . . . . . . . . . . . .
48
3.3 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
resumé 53 - references 53 - exercises 55
4 Local stability
57
4.1 Flows transport neighborhoods . . . . . . . . . . . . . . . .
57
4.2 Linear flows . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.3 Stability of flows . . . . . . . . . . . . . . . . . . . . . . . .
64
4.4 Stability of maps . . . . . . . . . . . . . . . . . . . . . . . .
67
resumé 70 - references 70 - exercises 72