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

TL;DR

This paper demonstrates that any minimal effective dynamical system on a Cantor set can be explicitly simulated by a minimal three-dimensional subshift of finite type, extending previous notions of simulation.

Contribution

It introduces a method to simulate minimal effective dynamical systems on Cantor sets using minimal 3D SFTs, generalizing Hochman's simulation concepts.

Findings

Any minimal effective system on a Cantor set can be simulated by a minimal 3D SFT.

Provides an explicit construction for such simulations.

Extends the theoretical framework of system simulation by subshifts.

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.