An Introduction to Dynamical Systems

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

Buch | Softcover

432 Seiten

1990
Cambridge University Press (Verlag)
978-0-521-31650-7 (ISBN)

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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.

Erscheint lt. Verlag	27.7.1990
Verlagsort	Cambridge
Sprache	englisch
Maße	173 x 247 mm
Gewicht	854 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-521-31650-2 / 0521316502
ISBN-13	978-0-521-31650-7 / 9780521316507
Zustand	Neuware