Examples for the Nonuniqueness of the Equilibrium State
Open Access
- 1 April 1977
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 228, 223-241
- https://doi.org/10.2307/1998528
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.Keywords
This publication has 2 references indexed in Scilit:
- Equilibrium States and the Ergodic Theory of Anosov DiffeomorphismsPublished by Springer Nature ,1975
- A Variational Principle for the Pressure of Continuous TransformationsAmerican Journal of Mathematics, 1975