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Classical and Quantum Chaos
Predrag Cvitanovi´c – Roberto Artuso – Per Dahlqvist – Ronnie Mainieri
– Gregor Tanner – G´abor Vattay – Niall Whelan – Andreas Wirzba
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version Feb 26 2002
printed June 19, 2002
osBook/ comments to: ******@
Contents
Contributors ................................. x
1 Overture 1
Why this book? ............................. 2
Chaos ahead .............................. 3
Agame of pinball ............................ 4
Periodic orbit theory .......................... 13
Evolution operators .......................... 18
From chaos to statistical mechanics .................. 22
Semiclassical quantization ....................... 23
Guide to literature ........................... 25
Guide to exercises ............................. 27
Resum´e .................................. 28
Exercises .................................. 32
2Flows 33
Dynamical systems ........................... 33
Flows .................................. 37
Changing coordinates ......................... 41
trajectories ......................... 44
Infinite-dimensional flows ....................... 45
Resum´e .................................. 50
Exercises .................................. 52
3Maps 57
Poincar´e sections ............................ 57
Constructing a Poincar´e section .................... 60
H´enon map ............................... 62
Billiards ................................. 64
Exercises .................................. 69
4 Local stability 73
Flows transport neighborhoods .................... 73
Linear flows ............................... 75
Nonlinear flows ............................. 80
Hamiltonian flows ........................... 82
i
ii CONTENTS
Billiards .....