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Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle (1202.6584v2)

Published 29 Feb 2012 in math.DS

Abstract: 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.