Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.
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.