TY  - BOOK
AU  - Geon Ho Choe 
TI  - Computational ergodic theory
T2  - Algorithms and Computation in Mathematics 
SN  - 9783540231219
AV  - QA313 
PY  - 2005///]
CY  - New York
PB  - Springer-Verlag
N1  - Chapter 1. Prerequisites
Chapter 2. Invariant Measures
Chapter 3. The Birkhoff Ergodic Theorem
Chapter 4. The Central Limit Theorem
Chapter 5. More on Ergodicity
Chapter 6. Homeomorphisms of the Circle
Chapter 7. Mod 2 Uniform Distribution
Chapter 8. Entropy
Chapter 9. The Lyapunov Exponent: One-Dimensional Case
Chapter 10. The Lyapunov Exponent: Multidimensional Case
Chapter 11. Stable and Unstable Manifolds
Chapter 12. Recurrence and Entropy
Chapter 13. Recurrence and Dimension
Chapter 14. Data Compression
N2  - Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society.---Summary provided by publisher
UR  - https://link.springer.com/book/10.1007/b138894
ER  -