JournalspmVol. 69 / No. 3DOI 10.4171/pm/1913

Equilibrium states and SRB-like measures of C1C^1-expanding maps of the circle

  • Eleonora Catsigeras

    Facultad de Ingenieria, Universidad de la República, Montevideo, Uruguay
  • Heber Enrich

    Facultad de Ingenieria, Universidad de la República, Montevideo, Uruguay
Equilibrium states and SRB-like measures of $C^1$-expanding maps of the circle cover

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Abstract

For any -expanding map of the circle we study the equilibrium states for the potential . We formulate a generalization of Pesin’s Entropy Formula that holds for all the Sinai–Ruelle–Bowen (SRB) measures if they exist, and for all the (necessarily existing) SRB-like measures. In the -generic case Pesin’s Entropy Formula holds for a unique SRB measure which is not absolutely continuous with respect to Lebesgue. The result also stands in the non-generic case for which no SRB measure exists.