Diffeomorphisms with Shadowable Measures

Abstract

In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the C 1 -interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity.

Keywords

• shadowing property
• pseudo-orbit
• shadowable measure
• Axiom A
• no-cycle condition
• strong transversality condition