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arXiv · 2105.07995

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

Silvère Gangloff·Piotr Oprocha
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Abstract

In this paper, we completely solve the problem when a Cantor dynamical system $(X,f)$ can be embedded in $\mathbb{R}$ with vanishing derivative everywhere. For this purpose, we construct a refining sequence of marked clopen partitions of $X$ 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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Silvère Gangloff, Piotr Oprocha. 2021-05-17. A Cantor dynamical system is slow if and only if all its finite orbits are attracting. https://arxiv.org/abs/2105.07995

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