Survey Of Nonlinear Dynamics ("Chaos Theory"), A - Hardcover

Ingraham, Richard L

Hardcover

ISBN 10: 9810207778 ISBN 13: 9789810207779

Publisher: World Scientific Publishing Co Pte Ltd, 1991

Synopsis

This book is intended to give a survey of the whole field of nonlinear dynamics (or “chaos theory”) in compressed form. It covers quite a range of topics besides the standard ones, for example, pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. The many meanings or measures of “chaos” in the literature are summarized. A precise definition of chaos based on a carefully limited sensitive dependence is offered. An application to quantum chaos is made. The treatment does not emphasize mathematical rigor but insists that the crucial concepts and theorems be mathematically well-defined. Thus topology plays a basic role. This alone makes this book unique among short surveys, where the inquisitive reader must usually be satisfied with colorful similes, analogies, and hand-waving arguments.Richard Ingraham graduated with B.S. summa cum laude in mathematics from Harvard college and with M.A. and Ph.D in Physics from Harvard Graduate School. He was granted the Sheldon Prize Traveling Fellowship by Harvard College and was a member of the Institute for Advanced Study at Princeton for two years.

About this title

Review

"This book gives a survey of the whole field of nonlinear dynamics (or "chaos theory") in compressed form. The author states the key definitions and theorems carefully. The book is very short, but its content is comprehensive. This book makes it possible for the reader to understand the main ideas in nonlinear dynamics and to proceed to further research along the lines of the cited literature." Si Ming Zhu Mathematical Reviews

Synopsis

This is a concise introduction to nonlinear dynamics (or "chaos theory"). Among the topics covered are pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. Various levels and meanings of chaos are summarized. The book does not stress mathematical rigour, but does insist that crucial concepts are mathematically defined. Thus topology plays a basic role.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 1991
• ISBN 10: 9810207778
• ISBN 13: 9789810207779
• Binding: Hardcover
• Language: English
• Number of pages: 118