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Classical and Quantumchaos

By Cvitanovi, Predrag

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Book Id: WPLBN0000660918
Format Type: PDF eBook
File Size: 5.60 MB
Reproduction Date: 2005
Full Text

Title: Classical and Quantumchaos  
Author: Cvitanovi, Predrag
Volume:
Language: English
Subject: Science., Mathematics, Logic
Collections:
Historic
Publication Date:
Publisher:

Citation

APA MLA Chicago

Cvitanovi, P. (n.d.). Classical and Quantumchaos. Retrieved from http://members.worldlibrary.net/


Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Averaging; Dynamical averaging; Evolution operators; Resume; and Exercises.

Table of Contents
Contents Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 1 Overture 1 1.1 Why this book? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Chaos ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 A game ofpin ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Periodic orbit theory . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.6 From chaos to statistical mechanics . . . . . . . . . . . . . . . . . . 20 1.7 Semiclassical quantization . . . . . . . . . . . . . . . . . . . . . . . 21 1.8 Guide to literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Guide to exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Resum?e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2 Trajectories 31 2.1 Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Infinite-dimensional flows . . . . . . . . . . . . . . . . . . . . . . . 40 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3 Local stability 51 3.1 Flows transport neighborhoods . . . . . . . . . . . . . . . . . . . . 51 3.2 Linear stability ofmaps . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3 Billiards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 Transporting densities 63 4.1 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2 Density evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Invariant measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.4 Evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Resum?e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73ii CONTENTS 5 Averaging 77 5.1 Dynamical averaging . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Evolution operators . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Resum?e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

 

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