When a physical-like measure is physical or SRB?

Abstract

For partially hyperbolic systems, we show that: (1) Integrable expanding along central bundle of all physical-like measures imply the set of physical-like is composed of finite ergodic hyperbolic SRB measures; (2) A physical-like measure with integrable expanding along central bundle is an ergodic hyperbolic SRB; (3) Quasi-conformal central bundle implies the set of physical-like measures is contained in the set of hyperbolic SRB measures and in particular implies the existence of physical measures.