Dynamical Systems

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.

Breadth of scope is unique Unlike many recent textbooks on chaotic systems no superficial treatment but 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 Includes supplementary material: sn.pub/extras

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

Contenu
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.