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

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.