Applied Symbolic Dynamics and Chaos

Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor.

Contents:

• Preface to the Second Edition
• Preface to the First Edition
• Introduction
• Symbolic Dynamics of Unimodal Maps
• Maps with Multiple Critical Points
• Symbolic Dynamics of Circle Maps
• Symbolic Dynamics of Two-Dimensional Maps
• Application to Ordinary Differential Equations
• Counting the Number of Periodic Orbits
• Symbolic Dynamics and Grammatical Complexity
• Symbolic Dynamics and Knot Theory
• Appendix
• References
• Index

Readership: Researchers and students interested in chaotic dynamics.
Key Features:

• No previous knowledge of dynamical systems theory is required in order to read this book
• The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps