This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.Read more
- Few other books on this subject
- Perfect for a masters course (includes many exercises)
- Author is well known in this area
Reviews & endorsements
'This is an excellent book for a one-semester course in ergodic theory … The overall presentation of the material is very appealing as it avoids pedantry and includes a variety of examples and exercises.' N. T. A. Haydn, ZAMMSee more reviews
'This is a very well-written book. It is well organised, clear, and coherent … It would also be suitable as a basis for a very good graduate course.' Hans Crauel, Bulletin of the London Mathematical Society
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: January 1998
- format: Paperback
- isbn: 9780521595346
- length: 192 pages
- dimensions: 227 x 153 x 11 mm
- weight: 0.29kg
- contains: 20 b/w illus.
- availability: Available
Table of Contents
1. Simple examples of equilibrium states
2. Some basic ergodic theory
4. Equilibrium states and pressure
5. Gibbs measures
6. Equilibrium states and derivatives
Appendix: Background material.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×