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On the limit quasi-shadowing property

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The second author is supported by NSFC (11471056) and Foundation and Frontier Research Program of Chongqing (cstc2016jcyjA0312).
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  • 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.

    Mathematics Subject Classification: Primary: 37C50; Secondary: 37D30.

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