C 2 -Stably Limit Shadowing Diffeomorphisms

Abstract EN

Let f be a diffeomorphism on a C ∞ closed surface.

In this paper, we show that if f has the C 2 -stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω ( f ) and if there is a dominated splitting on P s ( f ), then f satisfies both Axiom A and the strong transversality condition.