Examples for the nonuniqueness of the equilibrium state

Author:
Franz Hofbauer

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

MSC:
Primary 28A65

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

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

Article copyright:
© Copyright 1977
American Mathematical Society