Book Review

LC #: QA614

LCCN #: 95-51304 CIP

Author: Alligood, Kathleen T.

Title: Chaos:

Subtitle: an introduction to dynamical systems

Author: by Kathleen T. Alligood, Tim D. Sauer, and James A. Yorke.

Publisher: Springer, 1997.

Pagination: 603p

Other book information: bibl index afp

ISBN: 0-387-94677-2

Price: $39.00

Abstract: This exceptional introductory work is uniquely characterized by its combination of breadth and depth and by its pedagogical style of actively engaging the reader in exercises integral to theory development. The standard topics associated with the dynamical systems of maps and differential equations (stability and classification of equilibrium and fixed points, limit sets, chaos, fractals, bifurcations, etc.) receive a solid presentation. The carefully dissected proofs of the pivotal Poincare-Bendixson, Stable Manifold, and Cascade Theorems are unusual, and welcome, in an introductory book, as are the details about the important topic of state reconstruction from data. Extensive use is made of itineraries and transition graphs. The examples and exercises are excellent, especially the end-of-chapter "Challenges," extended exercises that, in stepwise fashion, lead the reader to deep results (e.g., period three implies chaos). There are computer experiments throughout for exploration of concepts through simulation. "Lab Visits," short reports on landmark experiments in the physical, chemical, and biological sciences, have citations to the research literature. Appendixes review relevant topics in linear algebra and discuss ordinary differential equation solvers along with codes. The exposition is clear, solid, and well illustrated. Very highly recommended. Upper-division undergraduates and graduate students.

Reviewer: G. J. G. Junevicus