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Chaotic Maps: Dynamics, Fractals and Rapid Fluctuations

Chaotic Maps: Dynamics, Fractals and Rapid Fluctuations


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About the Book

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


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Product Details
  • ISBN-13: 9781598299144
  • Publisher: Morgan & Claypool
  • Publisher Imprint: Morgan & Claypool
  • Depth: 13
  • Language: English
  • Returnable: Y
  • Spine Width: 13 mm
  • Weight: 476 gr
  • ISBN-10: 159829914X
  • Publisher Date: 19 Aug 2011
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 227
  • Series Title: Synthesis Lectures on Mathematics and Statistics
  • Sub Title: Dynamics, Fractals, and Rapid Fluctuations
  • Width: 191 mm


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