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Ergodic theory and dynamical systems

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Ergodic theory and dynamical systems/ by Yves Coudene ; translated by Reinie Erne.
作者:	Coudene, Yves.
其他作者:	Erne, Reinie.
出版者:	London :Springer London : : 2016.,
面頁冊數:	xiii, 190 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Ergodic theory. -
電子資源:	http://dx.doi.org/10.1007/978-1-4471-7287-1
ISBN:	9781447172871

Ergodic theory and dynamical systems
Coudene, Yves.

Ergodic theory and dynamical systems[electronic resource] /by Yves Coudene ; translated by Reinie Erne. - London :Springer London :2016. - xiii, 190 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Introduction -- Part I Ergodic Theory -- The Mean Ergodic Theorem -- The Pointwise Ergodic Theorem -- Mixing -- The Hopf Argument -- Part II Dynamical Systems -- Topological Dynamics -- Nonwandering -- Conjugation -- Linearization -- A Strange Attractor -- Part III Entropy Theory -- Entropy -- Entropy and Information Theory -- Computing Entropy -- Part IV Ergodic Decomposition -- Lebesgue Spaces and Isomorphisms -- Ergodic Decomposition -- Measurable Partitions and -Algebras -- Part V Appendices -- Weak Convergence -- Conditional Expectation -- Topology and Measures -- References.

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

ISBN: 9781447172871

Standard No.: 10.1007/978-1-4471-7287-1doiSubjects--Topical Terms:

672355
Ergodic theory.

LC Class. No.: QA313

Dewey Class. No.: 515.48

Ergodic theory and dynamical systems
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505 0 $a Introduction -- Part I Ergodic Theory -- The Mean Ergodic Theorem -- The Pointwise Ergodic Theorem -- Mixing -- The Hopf Argument -- Part II Dynamical Systems -- Topological Dynamics -- Nonwandering -- Conjugation -- Linearization -- A Strange Attractor -- Part III Entropy Theory -- Entropy -- Entropy and Information Theory -- Computing Entropy -- Part IV Ergodic Decomposition -- Lebesgue Spaces and Isomorphisms -- Ergodic Decomposition -- Measurable Partitions and -Algebras -- Part V Appendices -- Weak Convergence -- Conditional Expectation -- Topology and Measures -- References.
520 $a This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.
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