Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions

Ralph Abraham

ISBN 10: 1461273471 / ISBN 13: 9781461273479

Published by Springer-Verlag New York Inc., 2013

About this Item

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Bibliographic Details

• Title: Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions
• Publisher: Springer-Verlag New York Inc.
• Publication Date: 2013
• Language: English
• ISBN 10: 1461273471
• ISBN 13: 9781461273479
• Binding: Paperback / softback
• Condition: New
• Weight: 484 grams

About this title

Synopsis

Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed byMira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were

About the Author

Ralph Abraham is the author of "Dynamics: The Geometry of Behavior". He lives in California.