Weak measure expansivity of C2 dynamics

Abstract

Let ff be a C2{C}^{2}-diffeomorphism with Axiom A and no cycle condition on a two-dimensional smooth manifold. In this article, we prove that if ff is C2{C}^{2}-robustly weak measure expansive, then it is Q2{Q}^{2}-Anosov. Moreover, we expand the results of the C2{C}^{2}-diffeomorphism case into the C2{C}^{2}-vector field on a three-dimensional smooth manifold. Let XX be a C2{C}^{2}-vector field with Axiom A and no cycle condition. We prove that if XX is C2{C}^{2}-robustly weak measure expansive, then it is Q2{Q}^{2}-Anosov.

Keywords

• expansive
• weak measure expansive
• continuum-wise expansive
• q2-anosov
• axiom a
• primary 37c20
• 37c55
• 37d20