Equilibriums of some non-Hölder potentials
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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.References
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Additional Information
- Huyi Hu
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: hu@math.msu.edu
- Received by editor(s): January 9, 2006
- Received by editor(s) in revised form: June 10, 2006
- Published electronically: 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 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 2153-2190
- MSC (2000): Primary 37C40, 37A60; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9947-07-04412-1
- MathSciNet review: 2366978