Combinatorial Dynamics and Entropy in Dimension One

Llu??s Alsed??, Jaume Llibre;Michal Misiurewicz;;

• Publisher: WSPC
• Year: 2000
• eBook ISBN: 9789813105591
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Chaotic Behavior in Systems

This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.

Table of contents

• Contents
• Preface
• Chapter 1 Preliminaries
• Chapter 2 Interval maps
• Chapter 3 Circle maps
• Chapter 4 Entropy
• Chapter 5 Appendix: Graph maps
• Chapter 6 Appendix: Rotation Theory
• Bibliography
• List of symbols
• Index