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Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Equilibriums of some non-Hölder potentials

Author(s): Huyi Hu
Journal: Trans. Amer. Math. Soc. 360 (2008), 2153-2190.
MSC (2000): Primary 37C40, 37A60; Secondary 28D05
Posted: October 22, 2007
MathSciNet review: 2366978
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Abstract | References | Similar articles | Additional information

Abstract: We consider one-sided subshifts $ \sigma $ with some potential functions $ \varphi $ which satisfy the Hölder condition everywhere except at a fixed point and its preimages. We prove that the systems have conformal measures $ \nu $ and invariant measures $ \mu $ absolutely continuous with respect to $ \nu $, where $ \mu $ may be finite or infinite. We show that the systems $ (\sigma , \mu )$ are exact, and $ \mu $ are weak Gibbs measures and equilibriums for $ \varphi $. We also discuss uniqueness of equilibriums and phase transition.

These results can be applied to some expanding dynamical systems with an indifferent fixed point.

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Additional Information:

Huyi Hu
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: hu@math.msu.edu

DOI: 10.1090/S0002-9947-07-04412-1
PII: S 0002-9947(07)04412-1
Keywords: Potential, equilibrium, invariant measure, exactness, ergodicity, weak Gibbs measure
Received by editor(s): January 9, 2006
Received by editor(s) in revised form: June 10, 2006
Posted: October 22, 2007
Additional Notes: Part of this work was done when the author was at Penn State University and the University of Southern California. This work was supported by NSF under grants DMS-9970646 and DMS-0240097.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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