Topics in ergodic theory /
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| Author / Creator: | Sinaĭ, I͡A. G. (I͡Akov Grigorʹevich), 1935- |
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| Imprint: | Princeton, N.J. : Princeton University Press, 1994. |
| Description: | vi, 218 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Princeton mathematical series 44 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1610239 |
Table of Contents:
- I. General Ergodic Theory. Measurable Transformations. Invariant Measures. Ergodic Theorems. Lebesgue Spaces and Measurable 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
- II. Entropy Theory of Dynamical Systems. 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
- III. One-Dimensional Dynamics. Continued Fractions and Farey Fractions. Homeomorphisms and Diffeomorphisms of the Circle. Sharkovski's Ordering and Feigenbaum's Universality. Expanding Mappings of the Circie
- IV. Two-Dimensional Dynamics. Standard Map. Twist Maps. Periodic Orbits. Aubry-Mather Theory. Periodic Hyperbolic Points, Their Stable and Unstable Manifolds. Homoclinic and Heteroclinic Orbits. Homoclinic and Heteroclinic Points and Stochastic Layers
- V. Elements of the Theory of Hyperbolic Dynamical Systems. Geodesic Flows and Their Generalizations. Discontinuous Dynamical Systems. Stable and Unstable Manifolds. Existence of Local Manifolds. Gibbs Measures. Markov Partitions. Theorem for Dynamical Systems. Elements of Thermodynamic Formalism.