Chaotic Maps

Dynamics, Fractals, and Rapid Fluctuations
Erscheinungsjahr 2011
ISBN: 978-1-59829-914-4
Verlag: Morgan & Claypool Publishers

Buch, Englisch, 241 Seiten, Paperback, Format (B × H): 187 mm x 235 mm

Reihe: Synthesis Lectures on Mathematics and Statistics

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.

Autoren/Hrsg.

Inhaltsverzeichnis

- 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