Simulation of minimal effective dynamical systems on the Cantor sets by minimal tridimensional subshifts of finite type

Abstract

In this text, we prove then that any minimal effective dynamical system on a Cantor set $\mathcal{A}^{\mathbb{N}}$ can be simulated by a minimal $\mathbb{Z}^3$-SFT, in a sense that we explicit here. This notion is a generalization of simulation by factor and sub-action defined by Hochman.