Existence of Gibbs measures for countable Markov shifts

Author:
Omri Sarig

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1751-1758

MSC (2000):
Primary 37A99, 37D35; Secondary 37B10

DOI:
https://doi.org/10.1090/S0002-9939-03-06927-2

Published electronically:
January 2, 2003

MathSciNet review:
1955261

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a potential with summable variations and finite pressure on a topologically mixing countable Markov shift has a Gibbs measure iff the transition matrix satisfies the big images and preimages property. This strengthens a result of D. Mauldin and M. Urbanski (2001) who showed that this condition is sufficient.

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Additional Information

**Omri Sarig**

Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England

Email:
sarig@maths.warwick.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-03-06927-2

Keywords:
Gibbs measures,
countable Markov shifts,
thermodynamic formalism

Received by editor(s):
October 5, 2001

Published electronically:
January 2, 2003

Additional Notes:
This work is part of a Tel-Aviv University dissertation.

Communicated by:
Michael Handel

Article copyright:
© Copyright 2003
American Mathematical Society