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＜E-Book＞
Computational Ergodic Theory / by Geon Ho Choe
(Algorithms and Computation in Mathematics ; 13)

Edition	1st ed. 2005.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2005
Language	English
Size	XX, 453 p. 250 illus : online resource
Authors	*Choe, Geon Ho author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Mathematical physics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  All Subject Search FREE:Dynamical Systems FREE:Theoretical, Mathematical and Computational Physics FREE:Mathematical and Computational Engineering Applications
Notes	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 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 HTTP:URL=https://doi.org/10.1007/b138894

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