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Synopsis
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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Product Description
Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.
Review
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“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.” (Mário Bessa, Mathematical Reviews, Issue 2010 m)"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2009
- ISBN 10 3642019536
- ISBN 13 9783642019531
- BindingPaperback
- Number of pages290
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