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Cover: 9783642062070 | Computational Ergodic Theory | Geon Ho Choe | Taschenbuch | Paperback
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Computational Ergodic Theory
Taschenbuch von Geon Ho Choe
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
First textbook focusing on computational ergodic theory, thus making the topic more accessible to beginners than the standard ergodic theory textbooks
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Algorithms and Computation in Mathematics
Inhalt: xx
453 S.
250 s/w Illustr.
453 p. 250 illus.
ISBN-13: 9783642062070
ISBN-10: 3642062075
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Choe, Geon Ho
Auflage: Softcover reprint of hardcover 1st ed. 2005
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Algorithms and Computation in Mathematics
Maße: 235 x 155 x 26 mm
Von/Mit: Geon Ho Choe
Erscheinungsdatum: 21.10.2010
Gewicht: 0,715 kg
Artikel-ID: 107022983
Zusammenfassung
First textbook focusing on computational ergodic theory, thus making the topic more accessible to beginners than the standard ergodic theory textbooks
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Algorithms and Computation in Mathematics
Inhalt: xx
453 S.
250 s/w Illustr.
453 p. 250 illus.
ISBN-13: 9783642062070
ISBN-10: 3642062075
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Choe, Geon Ho
Auflage: Softcover reprint of hardcover 1st ed. 2005
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Algorithms and Computation in Mathematics
Maße: 235 x 155 x 26 mm
Von/Mit: Geon Ho Choe
Erscheinungsdatum: 21.10.2010
Gewicht: 0,715 kg
Artikel-ID: 107022983
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