Diffeomorphisms with C2 stable shadowing

Let f be a C-2 -diffeomorphism on a closed surface. In this paper, we show that if f satisfies shadowing stably in the C-2-topology, then (i) f is Kupka-Smale, (ii) if, in addition, the periodic points are dense in the non-wandering set and there is a dominated splitting on the closure of periodic points of saddle type, then f satisfies both Axiom A and the strong transversality condition.