This book presents a survey of the field of dynamical systems and its significance for research in complex systems and other fields, based on a careful analysis of specific important examples. It also explains the fundamental underlying mathematical concepts, with a particular focus on invariants of dynamical systems, including a systematic treatment of Morse-Conley theory. Entropy and related concepts in the topological, metric, measure theoretic and smooth settings and some connections with information theory are discussed, and cellular automata and random Boolean networks are presented as specific examples.

Autorentext

Jürgen Jost is a widely-known and successful textbook author. His textbooks with Springer see related literature.

Klappentext

Breadth of scope is unique

Author is a widely-known and successful textbook author

Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas

No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples

Includes a section on cellular automata

Inhalt

Stability of dynamical systems, bifurcations, and generic properties.- Discrete invariants of dynamical systems.- Entropy and topological aspects of dynamical systems.- Entropy and metric aspects of dynamical systems.- Entropy and measure theoretic aspects of dynamical systems.- Smooth dynamical systems.- Cellular automata and Boolean networks as examples of discrete dynamical systems.