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Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists J. M. T. Thompson, FRS, University College, London H. B. Stewart, Brookhaven National Laboratory This book is the first comprehensive, systematic account of nonlinear dynamics and chaos, one of the fastest-growing disciplines of applicable mathematics. It is highly illustrated and written in a clear, comprehensible style, progressing gently from the most elementary to the most advanced ideas while requiring little previous knowledge of mathematics. Examples of applications to a wide variety of scientific fields introduce concepts of instabilities, bifurcations and catastrophes, and particular attention is given to the vital new ideas of chaotic behaviour and unpredictability in deterministic systems. This is a book for systems analysts, for mathematicians, and for all those in any field of science or technology who use computers to model systems which change over time. Contents Preface 1 Introduction Part I Basic Concepts of Nonlinear Dynamics 2 An overview of nonlinear phenomena; 3 Point attractors in autonomous systems; 4 Limit cycles in autonomous systems; 5 Periodic attractors in driven oscillators; 6 Chaotic attractors in forced oscillators; 7 Stability and bifurcations of equilibria and cycles Part II Iterated Maps as Dynamical Systems 8 Stability and bifurcation of maps; 9 Chaotic behaviour of one- and two-dimensional maps Part III Flows, Outstructures, and Chaos 10 The geometry of recurrence; 11 The Lorenz system; 12 Rössler's band; 13 Geometry of bifurcation Part IV Applications in the Physical Sciences 14 Subharmonic resonances of an offshore structure; 15 Chaotic motions of an impacting system; 16 The particle accelerator and Hamiltonian dynamics; 17 Experimental observations of order and chaos References and Bibliography Index

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CHOICE Review

This monograph is a major contribution to the dissemination of the new goemetrical (topological) ideas and methods that are deepening and, perhaps, revolutionizing our understanding of nonlinear dynamical systems not only in the biological, social, and economic sciences but also in the traditionally mathematically treated areas of mechanics, physics (including chemical physics), and engineering. Thompson has been a major contributor to these ideas and methods that originated a century ago in the pioneering work of Henri Poincar;e. That earlier work focused on Hamiltonian (conservative) systems, in particular those associated with celestial mechanics; the recent developments emphasize the study of dissapative systems. Furthermore, modern work has been able to successfully integrate efforts in theoretical, computational, and, surprisingly, experimental work. The present volume brings a richness to the subject matter only hinted at by the work of Ren;e Thom and the range of applications studied, primarily in the physical sciences, will make this book attractive to a wide audience. An important distinction emphasized throughout is that ``... between those catastrophic bifurcations at which there is a finite rapid dynamic jump to a new steady state, and subtle bifurcations in which the change in response manifests itself in the smooth growth of a new local attractor after the bifurcation point.'' In addition to being well written, the book is unusually well illustrated. Recommended unreservedly.-M. Levinson, University of Maine