Advertisement

Ergodic Theory

  • I. P. Cornfeld
  • S. V. Fomin
  • Ya. G. Sinai

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 245)

Table of contents

  1. Front Matter
    Pages i-x
  2. Ergodicity and Mixing. Examples of Dynamical Systems

    1. Front Matter
      Pages 1-1
    2. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 3-42
    3. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 43-63
    4. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 64-95
    5. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 96-121
    6. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 122-137
    7. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 138-156
    8. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 157-177
    9. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 178-192
    10. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 193-224
  3. Basic Constructions of Ergodic Theory

    1. Front Matter
      Pages 225-225
    2. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 227-291
    3. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 292-321
  4. Spectral Theory of Dynamical Systems

    1. Front Matter
      Pages 323-323
    2. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 325-337
    3. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 338-355
    4. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 356-385
  5. Approximation Theory of Dynamical Systems by Periodic Dynamical Systems and Some of its Applications

    1. Front Matter
      Pages 387-387
    2. I. P. Cornfeld, S. V. Fomin, Ya. G. Sinai
      Pages 389-407
  6. Back Matter
    Pages 449-486

About this book

Introduction

Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna­ mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc­ tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Keywords

Elementary Analysis Ergodentheorie Ergodic theory ergodicity mixing

Authors and affiliations

  • I. P. Cornfeld
    • 1
  • S. V. Fomin
    • 1
  • Ya. G. Sinai
    • 1
  1. 1.Landau Institute of Theoretical PhysicsAcademy of SciencesMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-6927-5
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-6929-9
  • Online ISBN 978-1-4615-6927-5
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site
Industry Sectors
Pharma
Biotechnology
Finance, Business & Banking
IT & Software
Telecommunications
Consumer Packaged Goods
Aerospace
Oil, Gas & Geosciences
Engineering