Examples for the nonuniqueness of the equilibrium state

Hofbauer, Franz

doi:10.1090/S0002-9947-1977-0435352-1

Examples for the nonuniqueness of the equilibrium state
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by Franz Hofbauer

Trans. Amer. Math. Soc. 228 (1977), 223-241

DOI: https://doi.org/10.1090/S0002-9947-1977-0435352-1

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Abstract:

In this paper equilibrium states on shift spaces are considered. A uniqueness theorem for equilibrium states is proved. Then we study a particular class of continuous functions. We characterize the functions of this class which satisfy Ruelle’s Perron-Frobenius condition, those which admit a measure determined by a homogeneity condition, and those which have unique equilibrium state. In particular, we get examples for the nonuniqueness of the equilibrium state.

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