Author | Cornfeld, I. P. author |
---|---|
Title | Ergodic Theory [electronic resource] / by I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai |
Imprint | New York, NY : Springer New York, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6927-5 |
Descript | X, 486 p. online resource |
I Ergodicity and Mixing. Examples of Dynamic Systems -- 1 Basic Definitions of Ergodic Theory -- 2 Smooth Dynamical Systems on Smooth Manifolds -- 3 Smooth Dynamical Systems on the Torus -- 4 Dynamical Systems of Algebraic Origin -- 5 Interval Exchange Transformations -- 6 Billiards -- 7 Dynamical Systems in Number Theory -- 8 Dynamical Systems in Probability Theory -- 9 Examples of Infinite Dimensional Dynamical Systems -- II Basic Constructions of Ergodic Theory -- 10 Simplest General Constructions and Elements of Entropy Theory of Dynamical Systems -- 11 Special Representations of Flows -- III Spectral Theory of Dynamical Systems -- 12 Dynamical Systems with Pure Point Spectrum -- 13 Examples of Spectral Analysis of Dynamical Systems -- 14 Spectral Analysis of Gauss Dynamical Systems -- IV Approximation Theory of Dynamical Systems by Periodic Dynamical Systems and Some of its Applications -- 15 Approximations of Dynamical Systems -- 16 Special Representations and Approximations of Smooth Dynamical Systems on the Two-dimensional Torus -- Appendix 1 -- Lebesgue Spaces and Measurable Partitions -- Appendix 2 -- Relevant Facts from the Spectral Theory of Unitary Operators -- Appendix 3 -- Proof of the Birkhoff-Khinchin Theorem -- Appendix 4 -- Kronecker Sets -- Bibliographical Notes