Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Ergodic Theory of Random Transformations

  • Book
  • © 1986

Overview

Authors:
  1. Yuri Kifer

    1. Institute of Mathematics and Computer Science, Jerusalem, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Progress in Probability (PRPR, volume 10)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • Yuri Kifer
    Pages 1-6

  3. General analysis of random maps

    • Yuri Kifer
    Pages 7-32

  4. Entropy characteristics of random transformations

    • Yuri Kifer
    Pages 33-87

  5. Random bundle maps

    • Yuri Kifer
    Pages 88-129

  6. Further study of invariant subbundles and characteristic exponents

    • Yuri Kifer
    Pages 130-155

  7. Smooth random transformations

    • Yuri Kifer
    Pages 156-190

  8. Back Matter

    Pages 191-212
    Download chapter PDF
Back to top

Keywords

About this book

Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma­ tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. 'Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random matrices and stochastic flows generated by stochastic differential equations.

Authors and Affiliations

  • Institute of Mathematics and Computer Science, Jerusalem, Israel

    Yuri Kifer

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation