Positively weak measure expansive differentiable maps

摘要

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