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Transactions of the American Mathematical Society

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Examples for the nonuniqueness of the equilibrium state

Author: Franz Hofbauer
Journal: Trans. Amer. Math. Soc. 228 (1977), 223-241
MSC: Primary 28A65
MathSciNet review: 0435352
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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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