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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9947-03-03269-0
PII: S 0002-9947(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