Computational Ergodic Theory

Geon Hoe Choe - Collection Algorithms and Computation in Mathematics

454 pages, parution le 11/03/2005

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Résumé

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.

Written for: Graduate students and researchers in mathematics, physics, chemistry, data compression (electrical engineering), and biology

Sommaire

Prerequisites
Invariant Measures
The Birkhoff Ergodic Theorem
The Central Limit Theorem
More on Ergodicity
Homeomorphisms of the Circle
Mod 2 Uniform Distribution
Entropy
The Lyapunov Exponent: One-Dimensional Case
The Lyapunov Exponent: Multidimensional Case
Stable and Unstable Manifolds
Recurrence and Entropy
Recurrence and Dimension
Data Compression

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Geon Hoe Choe
Collection	Algorithms and Computation in Mathematics
Parution	11/03/2005
Nb. de pages	454
Format	16 x 24
Couverture	Relié
Poids	810g
Intérieur	Noir et Blanc
EAN13	9783540231219