SRB-like Measures for C⁰ Dynamics
For any continuous map f: M → M on a compact manifold M, we define SRB-like (or observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f always has observable measures, even if SRB measures do not exist. We prove that the definition of observability is optimal, provided that the purpose of the researcher is to describe the asymptotic statistics for Lebesgue almost all initial states. Precisely, the never empty set of all observable measures is...