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Chaotic Maps [electronic resource] : Dynamics, Fractals, and Rapid Fluctuations / by Goong Chen, Yu Huang.

By: Chen, Goong [author.].
Contributor(s): Huang, Yu [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2011Edition: 1st ed. 2011.Description: XIII, 227 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031024030.Subject(s): Mathematics | Statistics  | Engineering mathematics | Mathematics | Statistics | Engineering MathematicsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 510 Online resources: Click here to access online
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.
In: Springer Nature eBookSummary: 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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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.

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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