Topics in ergodic theory

by Sinaĭ, I︠A︡. G., (I︠A︡kov Grigorʹevich)

Type Book

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Title Statements

Full title :Topics in ergodic theory / Ya. G. Sinai.

Edition Statements

Publication Date:1994.

Publication Statements

Publisher(s):Princeton University Press
Place of Publication:Princeton, N.J
Language:eng
Publication Date:1994.

The Physical Object

Description:vi, 218 pages : : illustrations ; : 25 cm.

Edition Identifiers

ISBN:0691032777, 9780691032771
oclc:ocm27727728
LC Classification:QA611.5
Dewey Decimal:515/.42

Measurable transformations, invariant measures, ergodic theorems -- Lebesgue spaces and measureable partitions, ergodicity and decomposition into ergodic components, spectrum of interval exchange transformations -- Isomorphism of dynamical systems, generators of dynamical systems -- Dynamical systems with pure point spectra -- General properties of eigenfunctions and eigenvalues of ergodic automorphisms, isomorphism of dynamical systems with pure point spectrum -- Entropy theory of dynamical systems -- Breiman theorem, Pinsker partition, K-systems, exact endomorphisms, Gibbs measures -- Entropy of dynamical systems with multidimensional time, systems of cellular automata as dynamical systems -- Continued fractions and Farey fractions -- Homeomorphisms and diffeomorphisms of the circle -- Sharkovski's ordering and Feigenbaum's universality -- Expanding mappings of the circle -- Standard map, twist maps, periodic orbits, Aubrey-Mather theory -- Periodic hyperbolic points, their stable and unstable manifolds, homoclinic and heteroclinic orbits.

Homoclinic and heteroclinic points and stochastic layers -- Geodesic flows and their generalizations, discontinuous dynamical systems, stabl…