| Palis conjectured that typical system has a finite number of attractors,and each attractor has a finite number of physical measures（SRB measures）.The union of the basins of these physical measures is a full Lebesgue measure subset.In this paper,we discuss the existence,finiteness and basin full cover properties of physical measures for a class of partially hyperbolic systems in the non-invertible case.Let f be a C1+αnonsingular endomorphism on a compact smooth oriented Riemannian manifold M.Assuming that f is partially hyperbolic,with a uniformly expanding unstable cone field and a central-stable sub-bundle,we prove that if f satisfies the partial volume expansion property,there exists a finite number of physical measures,and the union of the basins of these physical measures is a full Lebesgue measure subset.This result is a generalization of[26]. |
