Lyapunov Exponents and Smooth Ergodic Theory

ISBN-13: 9780821829219 / Angielski / Miękka / 2001

Portugal Lisbon Luis (Instituto Superior Tecnico Barreira; University Park Yakov (Pennsylvania State University Pesin

Opis

This self-contained 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. 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 non-experts who wish to become familiar with the field.