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- W3100972894 abstract "Consider a topologically transitive countable Markov shift and, let $f$ be a summable potential with bounded variation and finite Gurevic pressure. We prove that there exists an equilibrium state $mu_{tf}$ for each $t > 1$ and that there exists accumulation points for the family $(mu_{tf})_{t>1}$ as $t to infty$. We also prove that the Kolmogorov-Sinai entropy is continuous at $infty$ with respect to the parameter $t$, that is $lim_{t to infty} h(mu_{tf})=h(mu_{infty})$, where $mu_{infty}$ is an accumulation point of the family $(mu_{tf})_{t>1}$. These results do not depend on the existence of Gibbs measures and, therefore, they extend results of cite{MaUr01} and cite{Sar99} for the existence of equilibrium states without the BIP property, cite{JMU05} for the existence of accumulation points in this case and, finally, we extend completely the result of cite{Mor07} for the entropy zero temperature limit beyond the finitely primitive case." @default.
- W3100972894 created "2020-11-23" @default.
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- W3100972894 date "2018-07-12" @default.
- W3100972894 modified "2023-10-14" @default.
- W3100972894 title "Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts" @default.
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- W3100972894 doi "https://doi.org/10.1090/tran/7291" @default.
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