Computational Ergodic Theory

• Main Author: Choe, Geon Ho (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Series: Algorithms and Computation in Mathematics, 13
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Physics.; Applied mathematics.; Engineering mathematics.; Dynamical Systems and Ergodic Theory.; Theoretical, Mathematical and Computational Physics.; Appl.Mathematics/Computational Methods of Engineering.

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...

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.