POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS

Abstract

In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.