Ergodic Theory
Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of met...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1982, 1982
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| Edition: | 1st ed. 1982 |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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