Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Ergodic Theory
  • Cited by 449
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
1983
Online ISBN:
9780511608728
DOI:
https://doi.org/10.1017/CBO9780511608728
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
Series:
Cambridge Studies in Advanced Mathematics (2)
Information

Book description

The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.

Reviews

‘What the contents list does not prepare you for is the very high standard of exposition. The scholarship involved in this work will be appreciated by workers in the field and by generations of research students. I personally think this is an excellent book. It is a book which can be explored at leisure and has a place in the library of anyone with a more than passing interest in ergodic theory.’

Source: Bulletin of the London Mathematical Society

‘ … an excellent introduction to several areas which are of interest both from the point of view of the mathematical scholar and from that of the research mathematician.’

Source: American Scientist

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Accessibility standard: Unknown

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.