C²-stably inverse shadowing diffeomorphisms

Abstract

Let f be a C 2 -diffeomorphism on a closed surface. In this article, we show that if f has the C 2 -stably inverse shadowing property with respect to the class of continuous methods then (i) f is Kupka-Smale, and (ii) if the periodic points are dense in the non-wandering set ( f ) and there is a dominated splitting on the closure of periodic points of the saddle type P h ( f ), then f satisfies both Axiom A and the strong transversality condition.