当且仅当康托动力系统的所有有限轨道都相互吸引时，康托动力系统是慢的

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-05-17 DOI:10.3934/dcds.2022007

Silvère Gangloff, P. Oprocha

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引用次数: 1

摘要

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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A Cantor dynamical system is slow if and only if all its finite orbits are attracting

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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