SRB-like Measures for C Dynamics
نویسنده
چکیده
For any continuous map f : M → M on a compact manifold M , we define the SRB-like probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f has SRB-like measures, even if SRB measures do not exist. We prove that the definition of SRB-like measures is optimal, provided that the purpose of the researcher is to describe the asymptotic statistics for Lebesgue almost every initial state. We prove that any isolated measure in the set O of SRBlike measures is SRB. Finally we conclude that if O is finite or countable infinite, then there exist (up to countable many) SRB measures such that the union of their basins cover M Lebesgue a.e. MSC2010: Primary 37A05; Secondary 28D05
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