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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0435352-1
PII: S 0002-9947(1977)0435352-1
Article copyright: © Copyright 1977 American Mathematical Society