Eventually Shadowable Points
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DOI: 10.1007/s12346-020-00367-4
Abstract: We study the eventually shadowable points namely points for which every pseudo orbit passing through then can be eventually shadowed (Good and Meddaugh in Ergod Theory Dyn Syst 38(1):143–154, 2018). We will prove the following… read more here.
Keywords: eventually shadowable; shadowable points; compact metric; eventual shadowing ... See more keywords
The Asymptotic Average Shadowing Property of Iterated Function Systems
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DOI: 10.1007/s40840-021-01184-x
Abstract: In this paper, we explore the asymptotic average shadowing property of iterated function systems. We show that for an iterated function system IFS $$(\mathscr {F})$$ such that one of $$\mathscr {F}$$ is surjective, the pseudo-orbital… read more here.
Keywords: average shadowing; iterated function; shadowing property; asymptotic average ... See more keywords
Chain Mixing, Shadowing Properties and Multi-transitivity
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DOI: 10.1007/s41980-019-00218-2
Abstract: We prove that a map f is chain mixing if and only if $$f^r\times f^s$$fr×fs is chain transitive for some positive integers r, s. We prove that a map which has the average shadowing property with… read more here.
Keywords: mixing shadowing; chain; average shadowing; shadowing property ... See more keywords
Suspensions of homeomorphisms with the two-sided limit shadowing property
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DOI: 10.1080/14689367.2019.1693506
Abstract: In this paper, we discuss the two-sided limit shadowing property for continuous flows defined in compact metric spaces. We analyse some of the results known for the case of homeomorphisms in the case of continuous… read more here.
Keywords: two sided; sided limit; property; shadowing property ... See more keywords
On the limit quasi-shadowing property
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DOI: 10.3934/dcds.2017123
Abstract: In this paper, we study the limit quasi-shadowing property for diffeomorphisms. We prove that any quasi-partially hyperbolic pseudoorbit \begin{document}$\{x_{i},n_{i}\}_{i∈ \mathbb{Z}}$\end{document} can be \begin{document}$\mathcal{L}^p$\end{document} -, limit and asymptotic quasi-shadowed by a points sequence \begin{document}$\{y_{k}\}_{k∈ \mathbb{Z}}$\end{document} .… read more here.
Keywords: begin document; limit quasi; document; quasi shadowing ... See more keywords
Diffeomorphisms with a generalized Lipschitz shadowing property
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DOI: 10.3934/dcds.2020346
Abstract: Shadowing property and structural stability are important dynamics with close relationship. Pilyugin and Tikhomirov proved that Lipschitz shadowing property implies the structural stability[ 5 ]. Todorov gave a similar result that Lipschitz two-sided limit shadowing… read more here.
Keywords: generalized lipschitz; diffeomorphisms generalized; property; shadowing property ... See more keywords
EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY
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DOI: 10.4134/jkms.j190453
Abstract: In this paper we present a measurable version of the Smale’s spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X… read more here.
Keywords: invariantly measure; eventually shadowing; shadowing property; measure expanding ... See more keywords