文档介绍：Classical and Quantum Chaos
Predrag Cvitanovi´c – Roberto Artuso – Freddy Christiansen – Per
Dahlqvist – Ronnie Mainieri – Hans Henrik Rugh – Gregor Tanner
– G´abor Vattay – Niall Whelan – Andreas Wirzba
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version Aug 6, 2000 printed August 24, 2000
osBook/ comments to: ******@
Contents
Contributors ................................. ii
1 Overture 1
Why this book? ............................. 2
Chaos ahead .............................. 3
A game ofpinball ............................ 4
Periodic orbit theory .......................... 12
Evolution operators .......................... 17
From chaos to statistical mechanics .................. 20
Semiclassical quantization ....................... 21
Guide to literature ........................... 23
Guide to exercises ............................. 25
Resum´e .................................. 26
Exercises .................................. 30
2 Trajectories 31
Flows .................................. 31
Maps ................................... 36
Infinite-dimensional flows ....................... 40
Exercises .................................. 47
3 Local stability 51
Flows transport neighborhoods .................... 51
Linear stability ofmaps ........................ 56
Billiards ................................. 56
Exercises .................................. 60
4 Transporting densities 63
Measures ................................ 64
Density evolution ............................ 65
Invariant measures ........................... 66
Evolution operators .......................... 68
Resum´e .................................. 72
Exercises .................................. 73
i
ii CONTENTS
5 Averaging 77
Dynamical averaging .......................... 77
Evolution operators .......................... 83
Resum´e .............................