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

Chen, Goong,Huang, Yu

ISBN 10: 159829914X / ISBN 13: 9781598299144

Verlag: Morgan & Claypool Publishers, 2011

Beschreibung

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Bestandsnummer des Verkäufers 3TWOWA001MTF

Bibliografische Details

• Titel: Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations (Synthesis Lectures on Mathematics and Statistics)
• Verlag: Morgan & Claypool Publishers
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 159829914X
• ISBN-13: 9781598299144
• Einband: paperback
• Zustand: Very Good

Über diesen Titel

Inhaltsangabe

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