Lyapunov Exponents and Smooth Ergodic Theory (University Lecture Series)

Description

"This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows).". "The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory.". "This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field."--BOOK JACKET.

First Sentence

The stability theory of differential equations is centered around the problem whether a given solution x(t) Rn of the equation x = F(x) (1.0.1) is stable under a small perturbation of either the initial condition x0 = x(0) or the function F (in an appropriate topology in the space of continuous functions; it is assumed that the solution x(t) is well-defined for all t 0).

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