Lectures on Lyapunov Exponents

Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.

Marcelo Viana (Author)

9781107081734, Cambridge University Press

Hardback, published 24 July 2014

215 pages, 8 b/w illus. 105 exercises
23.6 x 15.7 x 1.6 cm, 0.45 kg

The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.

Preface
1. Introduction
2. Linear cocycles
3. Extremal Lyapunov exponents
4. Multiplicative ergodic theorem
5. Stationary measures
6. Exponents and invariant measures
7. Invariance principle
8. Simplicity
9. Generic cocycles
10. Continuity
References
Index.

Subject Areas: Differential calculus & equations [PBKJ], Calculus & mathematical analysis [PBK], Mathematics [PB]