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

<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) $\end{document}</tex-math></inline-formula> can be embedded in id="M2">\begin{document}$ \mathbb{R} with vanishing derivative. For purpose construct refining sequence marked clopen partitions id="M3">\begin{document}$ X which is adapted to kind. It turns out that there huge class such systems.</p>