Chaotic maps : dynamics, fractals, and rapid fluctuations
著者
書誌事項
Chaotic maps : dynamics, fractals, and rapid fluctuations
（Synthesis lectures on mathematics and statistics, 11）
Morgan & Claypool, c2011
- : pbk
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注記
Includes bibliographical references (p. 217-222) and index
内容説明・目次
内容説明
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.
目次
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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