An Introduction to Dynamical Systems

This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time.

D. K. Arrowsmith (Author), C. M. Place (Author)

9780521316507, Cambridge University Press

Paperback, published 27 July 1990

432 pages
24.7 x 17.3 x 2.8 cm, 0.854 kg

' … a book which can be recommended unreservedly … the many exercises are particularly useful.' International Mathematical News

In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this 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, Anosov automorphism, the horseshoe diffeomorphism 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. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed.

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.

Subject Areas: Number theory [PBH]