Smooth Ergodic Theory for Endomorphisms: 1978 (Lecture Notes in Mathematics)

Smooth Ergodic Theory for Endomorphisms: 1978 (Lecture Notes in Mathematics)

by Min Qian (Author), Min Qian (Author), Shu Zhu (Contributor), Jian-Sheng Xie (Contributor)


Smooth ergodic theory of deterministic dynamical systems deals with the study of dynamical behaviors relevant to certain invariant measures under differentiable mappingsor ows. The relevance of invariantmeasures is that they describe the f- quencies of visits for an orbit and hence they give a probabilistic description of the evolution of a dynamical system. The fact that the system is differentiable allows one to use techniques from analysis and geometry. The study of transformationsand their long-termbehavior is ubiquitousin ma- ematics and the sciences. They arise not only in applications to the real world but also to diverse mathematical disciplines, including number theory, Lie groups, - gorithms, Riemannian geometry, etc. Hence smooth ergodic theory is the meeting ground of many different ideas in pure and applied mathematics. It has witnessed a great progress since the pioneering works of Sinai, Ruelle and Bowen on Axiom A diffeomorphisms and of Pesin on non-uniformly hyperbolic systems, and now it becomes a well-developed eld.


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More Information

Format: Illustrated
Pages: 300
Edition: 2009
Publisher: Springer
Published: 02 Sep 2009

ISBN 10: 3642019536
ISBN 13: 9783642019531

Media Reviews

From the reviews:

In the useful monograph under review the authors intend to assemble several topics in the classic ergodic theory of deterministic endomorphisms gathering the most important results available until the present time. ... should be of interest to mathematicians, postgraduate students and physicists working on this field. (Mario Bessa, Mathematical Reviews, Issue 2010 m)