Abstract
We investigated the dynamical relationship between asymptotic average shadow ing property and pointwise Lipschitz shadowing property on the sequence map and the limit map. Then, we have: (1)Suppose {gn } strongly uniformly converge to g · gn has asymptotic average shadowing property implies g has asymptotic average shadowing property. (2) Suppose {gn } strongly uniformly converge to g · gn has fine pointwise shadowing property implies g has pointwise Lipschitz shadowing property. The above results promote the theory development of asymptotic average shadowing property and pointwise Lipschitz shadowing property.
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