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