Uniqueness of Minimizer for Countable Markov Shifts and Equidistribution of Periodic Points

研究成果: Article査読

抄録

For a finitely irreducible countable Markov shift and a potential with summable variations, we provide a condition on the associated pressure function which ensures that Bowen’s Gibbs state, the equilibrium state, and the minimizer of the level-2 large deviations rate function are all unique and they coincide. From this, we deduce that the set of periodic points weighted with the potential equidistributes with respect to the Gibbs-equilibrium state as the periods tend to infinity. Applications are given to the Gauss map, and the Bowen-Series map associated with a finitely generated free Fuchsian group with parabolic elements.

本文言語English
ページ(範囲)2415-2431
ページ数17
ジャーナルJournal of Statistical Physics
181
6
DOI
出版ステータスPublished - 2020 12

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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