\(C^2\)-stably limit shadowing diffeomorphisms (Q304962)

Summary: Let \(f\) be a diffeomorphism on a \(C^\infty\) 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 \(\Omega (f)\) and if there is a dominated splitting on \(P_s(f)\), then \(f\) satisfies both Axiom \(A\) and the strong transversality condition.