Equilibrium States and SRB-like measures of C Expanding Maps of the Circle
نویسنده
چکیده
For any C expanding map f of the circle we study the equilibrium states for the potential ψ = − log |f ′|. We formulate a C 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 C-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. Math. Subj. Class. (2010): Primary 37A05; Secondary 28D05.
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