Thermodynamic formalism for countable to one Markov systems

Author:
Michiko Yuri

Journal:
Trans. Amer. Math. Soc. **355** (2003), 2949-2971

MSC (2000):
Primary 28D99, 28D20, 58C40, 58E30, 37A40, 37A30, 37C30, 37D35, 37F10, 37A45

DOI:
https://doi.org/10.1090/S0002-9947-03-03269-0

Published electronically:
March 19, 2003

MathSciNet review:
1975407

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Abstract: For countable to one transitive Markov systems we establish thermodynamic formalism for non-Hölder potentials in nonhyperbolic situations. We present a new method for the construction of conformal measures that satisfy the weak Gibbs property for potentials of weak bounded variation and show the existence of equilibrium states equivalent to the weak Gibbs measures. We see that certain periodic orbits cause a phase transition, non-Gibbsianness and force the decay of correlations to be slow. We apply our results to higher-dimensional maps with indifferent periodic points.

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Additional Information

**Michiko Yuri**

Affiliation:
Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062-8520, Japan

Email:
yuri@math.sci.hokudai.ac.jp, yuri@mail-ext.sapporo-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-03-03269-0

Received by editor(s):
March 28, 2002

Received by editor(s) in revised form:
September 10, 2002

Published electronically:
March 19, 2003

Article copyright:
© Copyright 2003
American Mathematical Society