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Basic Ergodic Theory

Basic Ergodic Theory

., Birkhäuser Advanced Texts Basler Lehrbücher
 Taschenbuch
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1 The Poincaré 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.
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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Produktdetails

Autor: N. G. Nadkarni
ISBN-13: 9783034897952
ISBN: 3034897952
Einband: Taschenbuch
Seiten: 150
Gewicht: 260 g
Format: 235x155x mm
Sprache: Englisch

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Autor: N. G. Nadkarni
ISBN-13:: 9783034897952
ISBN: 3034897952
Verlag: Springer, Basel, Birkhäuser Basel
Gewicht: 260g
Seiten: 150
Sprache: Englisch
Auflage Softcover reprint of the original 1st ed. 1995
Sonstiges: Taschenbuch, 235x155x mm, IX, 150 p.