This book is the first comprehensive introduction to smooth ergodic
theory. It consists of two parts: the first introduces the core of
the theory and the second discusses more advanced topics. In
particular, the book describes the general theory of Lyapunov
exponents and its applications to the stability theory of
differential equations, the concept of nonuniform hyperbolicity,
stable manifold theory (with emphasis on the absolute continuity of
invariant foliations), and the ergodic theory of dynamical systems
with nonzero Lyapunov exponents. The authors also present a
detailed description of all basic examples of conservative systems
with nonzero Lyapunov exponents, including the geodesic flows on
compact surfaces of nonpositive curvature. This book is aimed at
graduate students specialising in dynamical systems and ergodic
theory as well as anyone who wants to acquire a working knowledge
of smooth ergodic theory and to learn how to use its tools. With
more than 80 exercises, the book can be used as a primary textbook
for an advanced course in smooth ergodic theory. The book is
self-contained and only a basic knowledge of real analysis, measure
theory, differential equations, and topology is required and, even
so, the authors provide the reader with the necessary background
definitions and results.
General
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