Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle

Details Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle

2012-02-29

arxiv.org/abs/1202.6584v1

Mathematics

Dynamical Systems

Scientific paper

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 the 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 the 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.

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