An Introduction to Dynamical Systems [Paperback]

This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time.Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit chaotic behavior .Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit chaotic behavior .Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit chaotic behavior. The first portion of the book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms and the logistic map and area-preserving planar maps. The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. The text contains many worked examples and exercises, many with hints. It will be a valuable first textbook for senior undergraduate and postgraduate students of mathematics, physics, and engineering.Preface; 1. Diffeomorphisms and flows; 2. Local properties of flow and diffeomorphims; 3. Structural stability, hyperbolicity and homoclinic points; 4. Local bifurcations I: planar vector fields and diffeomorphisms on R; 5. Local bifurcations II: diffeomorphisms on R2; 6. Area-preserving maps and their perturbations; Hints for exercises; References; Index. ...a very good textbook. It brings the reader in a short time through the fundamental ideas underlying the theory of dynamical systems theory. Mathematical Reviews ...a good textbook on the subject. Physics in Canada ...a true introduction to the modern theory of dynamilÓe