GENERIC DIFFEOMORPHISM WITH SHADOWING PROPERTY ON TRANSITIVE SETS

Abstract

Let f : M → M be a diffeomorphism on a closed C∞ manifold. Let Λ be a transitive set. In this paper, we show that (i) C 1-generically, f has the shadowing property on a locally maximal Λ if and only if Λ is hyperbolic, (ii) f has the C 1-stably shadowing property on Λ if and only if Λ is hyperbolic.

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