Equilibrium States and SRB-like measures of C1 Expanding Maps of the   Circle
  For any C1 expanding map f of the circle we study the equilibrium states for the potential -log |f'|. We formulate a C1 generalization of Pesin's Entropy Formula that holds for all the SRB measures if they exist, and for all the (necessarily existing) SRB-like measures. In the C1-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. 
Eleonora Catsigeras and Heber Enrich
math.DS