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Foundations of ergodic theory

By: Contributor(s): Material type: TextTextSeries: Cambridge studies in advanced mathematicsPublication details: Cambridge Cambridge University Press 2016Description: xvi, 530 pISBN:
  • 9781107126961
Subject(s): DDC classification:
  • 515.48 V4F6
Summary: Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book. The authors' friendly explanations and use of examples make complex concepts easy to follow Self-contained so it can easily be adapted to a graduate or undergraduate course Contains more than 400 exercises, many with hints and solutions. http://admin.cambridge.org/aq/academic/subjects/mathematics/abstract-analysis/foundations-ergodic-theory?format=HB
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1378 (0 Floor, East Wing) Non-fiction General Stacks 515.48 V4F6 (Browse shelf(Opens below)) Available 193293

Table of Contents

Preface
1. Recurrence
2. Existence of invariant measures
3. Ergodic theorems
4. Ergodicity
5. Ergodic decomposition
6. Unique ergodicity
7. Correlations
8. Equivalent systems
9. Entropy
10. Variational principle
11. Expanding maps
12. Thermodynamical formalism
Appendix. Topics of measure theory, topology and analysis
Hints or solutions for selected exercises
References
Index.

Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.

The authors' friendly explanations and use of examples make complex concepts easy to follow
Self-contained so it can easily be adapted to a graduate or undergraduate course
Contains more than 400 exercises, many with hints and solutions.

http://admin.cambridge.org/aq/academic/subjects/mathematics/abstract-analysis/foundations-ergodic-theory?format=HB

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