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Basic Ergodic Theory

Author: M G Nadkarni
Publisher: Basel : Birkhäuser Basel : Imprint : Birkhäuser, 1995.
Series: Birkhäuser Advanced Texts, Basler Lehrbücher.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Database:WorldCat
Summary:
This is an introductory book on ergodic theory. The presentation has a slow pace and the book can be read by anyone with a background in basic measure theory and metric topology. In particular, the first two chapters, the elements of ergodic theory, can form a course of four to six lectures at the advanced undergraduate or the beginning graduate level. A new feature of the book is that the basic topics of ergodic  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M G Nadkarni
ISBN: 9783034888394 3034888392
OCLC Number: 851815500
Description: 1 online resource (ix, 150 pages).
Contents: 1 The Poincare Recurrence Lemma.- 2 Ergodic Theorems of Birkhoff and von Neumann.- 3 Ergodicity.- 4 Mixing Conditions and Their Characterisations.- 5 Bernoulli Shift and Related Concepts.- 6 Discrete Spectrum Theorem.- 7 Induced Automorphisms and Related Concepts.- 8 Borel Automorphisms are Polish Homeomorphisms.- 9 The Glimm-Effros Theorem.- 10 E. Hopf's Theorem.- 11 H Dye's Theorem.- 12 Flows and Their Representations.- References.
Series Title: Birkhäuser Advanced Texts, Basler Lehrbücher.
Responsibility: by M.G. Nadkarni.

Abstract:

This is an introductory book on ergodic theory. The presentation has a slow pace and the book can be read by anyone with a background in basic measure theory and metric topology. In particular, the first two chapters, the elements of ergodic theory, can form a course of four to six lectures at the advanced undergraduate or the beginning graduate level. A new feature of the book is that the basic topics of ergodic theory such as the Poincaré recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem are discussed, topics which have so far not found a place in texts on ergodic theory. In this second edition, a section on rank one automorphisms and a brief discussion of the ergodic theorem due to Wiener and Wintner have been added. "This relatively short book is, for anyone new to ergodic theory, admirably broad in scope. The exposition is clear, and the brevity of the book has not been achieved by giving terse proofs. The examples have been chosen with great care. Historical facts and many references serve to help connect the reader with literature that goes beyond the content of the book as well as explaining how the subject developed. It is easy to recommend this book for students as well as anyone who would like to learn about the descriptive approach to ergodic theory." (Summary of a review of the first edition in Math Reviews).

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"This relatively short book is, for anyone new to ergodic theory, admirably broad in scope. The exposition is clear, and the brevity of the book has not been achieved by giving terse proofs. The Read more...

 
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