{"title":"A Cantor dynamical system is slow if and only if all its finite orbits are attracting","authors":"Silvère Gangloff, P. Oprocha","doi":"10.3934/dcds.2022007","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this paper we completely solve the problem of when a Cantor dynamical system <inline-formula><tex-math id=\"M1\">\\begin{document}$ (X, f) $\\end{document}</tex-math></inline-formula> can be embedded in <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\mathbb{R} $\\end{document}</tex-math></inline-formula> with vanishing derivative. For this purpose we construct a refining sequence of marked clopen partitions of <inline-formula><tex-math id=\"M3\">\\begin{document}$ X $\\end{document}</tex-math></inline-formula> which is adapted to a dynamical system of this kind. It turns out that there is a huge class of such systems.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"100 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Continuous Dynamical Systems - S","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2022007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we completely solve the problem of when a Cantor dynamical system \begin{document}$ (X, f) $\end{document} can be embedded in \begin{document}$ \mathbb{R} $\end{document} with vanishing derivative. For this purpose we construct a refining sequence of marked clopen partitions of \begin{document}$ X $\end{document} which is adapted to a dynamical system of this kind. It turns out that there is a huge class of such systems.
In this paper we completely solve the problem of when a Cantor dynamical system \begin{document}$ (X, f) $\end{document} can be embedded in \begin{document}$ \mathbb{R} $\end{document} with vanishing derivative. For this purpose we construct a refining sequence of marked clopen partitions of \begin{document}$ X $\end{document} which is adapted to a dynamical system of this kind. It turns out that there is a huge class of such systems.
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