Computational Ergodic Theory

Portada
Springer Science & Business Media, 11 feb 2005 - 453 páginas

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.

 

Índice

Prerequisites
1
Invariant Measures
47
The Birkhoff Ergodic Theorem
85
The Central Limit Theorem
133
More on Ergodicity
155
Homeomorphisms of the Circle
183
Uniform Distribution
207
8
237
Multidimensional Case
299
Stable and Unstable Manifolds
333
mapping
349
Recurrence and Entropy
363
Recurrence and Dimension
391
Data Compression
417
References
439
Index 449
448

OneDimensional Case
269

Otras ediciones - Ver todo

Términos y frases comunes

Información bibliográfica