On the limit quasi-shadowing property
Fang Zhang Yunhua Zhou
Discrete & Continuous Dynamical Systems - A 2017, 37(5): 2861-2879 doi: 10.3934/dcds.2017123

In this paper, we study the limit quasi-shadowing property for diffeomorphisms. We prove that any quasi-partially hyperbolic pseudoorbit $\{x_{i},n_{i}\}_{i∈ \mathbb{Z}}$ can be $\mathcal{L}^p$-, limit and asymptotic quasi-shadowed by a points sequence $\{y_{k}\}_{k∈ \mathbb{Z}}$. We also investigate the $\mathcal{L}^p$-, limit and asymptotic quasi-shadowing properties for partially hyperbolic diffeomorphisms which are dynamically coherent.

keywords: limit quasi-shadowing quasi-partially hyperbolic pseudoorbit partial hyperbolicity dynamical coherence

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