Diffeomorphisms with the s-limit shadowing property

Abstract

Let Diff(M) be the space of diffeomorphisms of a closed C ∞ manifold M endowed with the C 1-topology, and denote by ℛ(f) the chain recurrent set of f ∈ Diff(M). In this article, we show that C 1-generically f |ℛ(f) has the s-limit shadowing property if and only if f satisfies both Axiom A and no-cycle condition.