Topological entropy for positively weak measure expansive shadowable maps

Abstract

In this paper, we consider positively weak measure expansive homeomorphisms and flows with the shadowing property on a compact metric space X. Moreover, we prove that if a homeomorphism (or flow) has a positively weak expansive measure and the shadowing property on its nonwandering set, then its topological entropy is positive.

Keywords

• shadowing property
• expansive
• positively measure expansive
• positively weak measure expansive
• topological entropy
• 37c50
• 37d20
• 37b40