عنوان

Basic Ergodic Theory

شابک

3034888392

شابک

9783034888394

شماره

b556548

عنوان اصلي

Basic Ergodic Theory

نام عام مواد

[Book]

نام نخستين پديدآور

by M.G. Nadkarni.

وضعيت ويراست

Second edition

محل نشرو پخش و غیره

Basel

نام ناشر، پخش کننده و غيره

Birkhäuser Basel : Imprint : Birkhäuser

تاریخ نشرو بخش و غیره

1995

نام خاص و کميت اثر

(ix, 150 pages)

عنوان فروست

Birkhäuser Advanced Texts, Basler Lehrbücher.

متن يادداشت

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.

متن يادداشت

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).

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by M.G. Nadkarni.

مستند نام اشخاص تاييد نشده

M G Nadkarni

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y