C~2-stably inverse shadowing diffeomorphisms

摘要

Let/be a C~2-diffeomorphism on a closed surface. In this article, we show that if/ has the C~2-stably inverse shadowing property with respect to the class of continuous methods then (i)/is Kupka-Smale, and (ii) if the periodic points are dense in the non-wandering set Ω(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.