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Algorithms and Computation in Mathematics #13: Computational Ergodic Theory

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Algorithms and Computation in Mathematics #13: Computational Ergodic Theory Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

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.- References.- Index.

Product Details

ISBN:
9783540231219
Author:
Choe, Geon Ho
Publisher:
Springer
Author:
Choe, Geon H.
Subject:
Differential Equations
Subject:
Applied
Subject:
Mathematical Physics
Subject:
Entropy
Subject:
Ergodic theory
Subject:
DYNAMICAL SYSTEMS
Subject:
Lyapunov exponent
Subject:
Maple simulations
Subject:
Dynamical Systems and Ergodic Theory
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics-Differential Equations
Subject:
Mathematical Analysis
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Algorithms and Computation in Mathematics
Series Volume:
13
Publication Date:
May 2005
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
473
Dimensions:
235 x 155 mm

Related Subjects

Engineering » Engineering » General Engineering
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » General
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Algorithms and Computation in Mathematics #13: Computational Ergodic Theory New Hardcover
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