Graph covers of higher dimensional dynamical systems (Q2673849)

In this paper, an inverse sequence of graph covers is extended from zero-dimensional dynamical systems to arbitrary dynamical systems. Let us recall that an inverse sequence \(\mathcal{G}=\{(G_i,\phi_i); i\in \mathbb{N})\) is called an inverse sequence of graph homeomorphisms if, for every \(i\in \mathbb{N}\), \(\phi_i:G_i\to G_{i-1}\) is a graph homeomorphism. If in addition \(\phi_i\) is a graph cover, then \(\mathcal{G}\) will be called an inverse sequence of graph covers. The following is the first main result obtained in this paper. Theorem. A surjective dynamical system is zero-dimensional iff it is conjugate to an inverse limit of graph covers. The second main result is the following: Theorem. Every dynamical system is conjugate to the system defined by inverse sequence of twinned graph homomorphisms.