Equilibriums of some non-Hölder potentials

Hu, Huyi

doi:10.1090/S0002-9947-07-04412-1

Equilibriums of some non-Hölder potentials
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Trans. Amer. Math. Soc. 360 (2008), 2153-2190 Request permission

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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