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
Les mer
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
Les mer
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.
Les mer
Produktdetaljer
ISBN
9783031012754
Publisert
2011-08-18
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
191 mm
Aldersnivå
Professional/practitioner, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Orginaltittel
Chaotic Maps