During the talk we will focus on surjective Cantor systems. Each such system can be easily embedded in the Gehman dendrite, as its set of endpoints is a Cantor set. We will show that for each such embedding there exists a mixing map of the dendrite such that the endpoints’ subsystem is conjugate to the Cantor system of choice. The main tool to obtain this result follows from Shimomura’s method of approximating the dynamics on zero dimensional systems by analysing the dynamics of coverings of the underlying space. We will discuss the dynamical properties of the constructed map.

The talk is based on joint work with Dominik Kwietniak and Piotr Oprocha.