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.
Rezensionen / Stimmen
"This book provides a survey of various topics of dynamical systems. Applications of both the concepts and the results are presented.
The author takes the opportunity to explain the underlying fundamental mathematical concepts involved in the results, for example the Conley-Floer theory, which is a topic that is not commonly studied in introductory texts on dynamical systems. The book studies entropy and related concepts within topological, metric, measure theoretic and smooth settings, giving connections with information theory, cellular automata and Boolean networks.
The book is written in a careful style. Most of the results are given without proof, though the necessary references for them are included. Many of the results are illustrated through carefully chosen examples." (Sergio Plaza, Mathematical Reviews)
