Dynamical Systems: Examples of Complex Behaviour / Edition 1

by Jürgen Jost

Overview

Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in specific examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical refinements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively different dynamics, and to studytransitions between different types. Itis also important to find out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some final or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyof theconceptstobeintroducedareusefulineither case.

Product Details

ISBN-13:	9783540229087
Publisher:	Springer Berlin Heidelberg
Publication date:	09/12/2005
Series:	Universitext
Edition description:	2005
Pages:	190
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

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

Table of Contents

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.

Editorial Reviews

"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)

From the Publisher