Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations (Synthesis Lectures on Mathematics and Statistics) - Softcover

Chen, Goong; Huang, Yu

Softcover

ISBN 10: 159829914X ISBN 13: 9781598299144

Publisher: Morgan & Claypool Publishers, 2011

Synopsis

This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations.

Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on R^N / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

Edition details

• Publisher: Morgan & Claypool Publishers
• Publication date: 2011
• Language: English
• ISBN 10: 159829914X
• ISBN 13: 9781598299144
• Binding: Paperback
• Number of pages: 242