ASYMPTOTIC AVERAGE SHADOWING PROPERTY ON A CLOSED SET

Abstract

Let f be a difeomorphism of a closed n -dimensional smooth manifold M, and p be a hyperbolic periodic point of f. Let Λ(p) be a closed set which containing p. In this paper, we show that (i) if f has the asymptotic average shadowing property on Λ(p), then Λ(p) is the chain component which contains p. (ii) suppose f has the asymptotic average shadowing property on Λ(p). Then if f |Λ(p) has the C 1-stably shadowing property then it is hyperbolic.

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