Weak Chaos and Quasi-Regular Patterns

by Georgin Moiseevich Zaslavskiî, R. Z. Sagdeev, D. A. Usikov, A. A. Chernikov, A. R. Sagdeeva

Overview

This book presents the fundamentals of chaos theory in conservative systems and provides a systematic study of the theory of transitional states of physical systems that lie between deterministic and chaotic behavior. The authors begin with the general concepts of Hamiltonian dynamics, stabililty, and chaos, and then discuss the theory of stochastic layers and webs and the numerous applications of this theory, particularly to pattern symmetry. Throughout, they are meticulous in providing a detailed presentation of the material, which enables the reader to learn the necessary computational methods and to apply them to other problems. The inclusion of computer graphics will aid understanding and the final section of the book contains a collection of patterns in art and living nature that will fascinate.

Product Details

ISBN-13:	9780521373173
Publisher:	Cambridge University Press
Publication date:	04/11/1991
Series:	Cambridge Nonlinear Science Series , #1
Pages:	268
Product dimensions:	6.22(w) x 9.29(h) x 0.79(d)

Table of Contents

Part I. General Concepts: Hamiltonian dynamics; Stability and chaos; Part II. Dymanic Order and Choas: The stochastic layer; Stochastic layer - stochastic sea transition; The stochastic web; Uniform web; Part III. Spatial Patterns: Two-dimensional patterns with quasi-symmetry; Two-dimensional hydrodynamic patterns with symmetry and quasi-symmetry; Chaos and streamlines; Part IV. Miscellanea: Patterns in art and nature; References; Index.

Editorial Reviews

"The serious student of chaos will find this book well worth reading. As a technical review, it is presently unparalleled, and as a provocative introduction to the mysteries of patterns, it is unique." Ronald F. Fox, American Journal of Physics

"...will be of most interest to specialists looking for a source for this material outside the original literature - the only other place much of it can be found." C. Eugene Wayne, Physics Today

"The material in this book can, and should, be incorporated into a senior undergraduate, or first year graduate, mechanics course. This is also an interesting and very readable book for physicists and applied mathematicians who are interested in chaos, irreversibility, and theories of spatial patterns and symmetries. I recommend this book highly...." K.K. Lee, Physics in Canada

"a stimulating book that can provide new ideas on the generation and occurrence of patterns is a wide range of situations." Peter J. Bryant, SIAM Review

From the Publisher