Renormalisation in Area-Preserving Maps

Renormalisation in Area-Preserving Maps

by R.S. S. MacKay
     
 

ISBN-10: 9810213719

ISBN-13: 9789810213718

Pub. Date: 08/28/1993

Publisher: World Scientific Publishing Company, Incorporated

This book is adapted and revised from the author's seminal PhD thesis, in which two forms of asymptotically universal structure were presented and explained for area-preserving maps. Area-preserving maps are the discrete-time analogue of two degree-of-freedom Hamiltonian systems. How they work and much of their dynamics are described in this book. The…  See more details below

Overview

This book is adapted and revised from the author's seminal PhD thesis, in which two forms of asymptotically universal structure were presented and explained for area-preserving maps. Area-preserving maps are the discrete-time analogue of two degree-of-freedom Hamiltonian systems. How they work and much of their dynamics are described in this book. The asymptotically universal structure is found on small scales in phase-space and long time-scales. The key to understanding it is renormalisation, that is, looking at a system on successively smaller phase-space and longer time scales. Having presented this idea, the author briefly surveys the use of the idea of renormalisation in physics. The renormalisation picture is then presented as the key to understanding the transition from regular to chaotic motion in area-preserving maps. Although written ten years ago, the subject matter continues to interest many today. This updated version will be useful to both researchers and students.

Read More

Product Details

ISBN-13:
9789810213718
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
08/28/1993
Series:
Advanced Series in Nonlinear Dynamics, #6
Pages:
324

Table of Contents

Preface
Abstract
Acknowledgements
Ch. 1Introduction to Area Preserving Maps1
1.1Conservative Systems and Area Preserving Maps1
1.2Periodic Orbits27
1.3Invariant Circles69
1.4Stochastic Behaviour85
Ch. 2Introduction to Renormalisation98
2.1Renormalisation in Physics98
2.2Renormalisation in Dynamical Systems102
2.3Renormalisation Techniques111
Ch. 3Period Doubling in Area Preserving Maps126
3.1Period Doubling Sequences126
3.2Renormalisation139
3.3The Universal One Parameter Family144
3.4Appendices155
Ch. 4Renormalisation for Invariant Circles161
4.1Renormalisation161
4.2Fixed Point Analysis166
4.3Simple Fixed Point174
4.4Critical Fixed Point193
4.5The Universal One Parameter Family225
4.6Discussion245
4.7Renormalisation for Maps on a Circle251
Summary290
Problems for the future290
References294
Supplementary reference list301

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >