The Research of Asymptotic Average Shadowing Property and Pointwise Lipschitz Shadowing Property

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.