Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations

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

• 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 RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

Book Details

• Authors: Goong Chen, Yu Huang
• Publisher: Morgan & Claypool Publishers
• eBook ISBN: 9781598299151, 1598299158
• Print ISBN: 9781598299144, 159829914X