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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 partitionsof $X$ which is adapted to a dynamical system of this kind. It turns out thatthere is a huge class of such systems.

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