Dynamical systems of finite-dimensional metric spaces and zero-dimensional covers (Q1939219)

It is said that a dynamical system \((Y,g)\) \textit{covers} \((X,f)\) via an onto map \(p:Y\longrightarrow X\) provided that \(p\circ g=f\circ p\). In this paper, the authors, improving and generalizing a theorem by \textit{J. Kulesza} [Ergodic Theory Dyn. Syst. 15, No. 5, 939--950 (1995; Zbl 0882.54034)] to nonseparable metric spaces, prove the following main result: every metric \(n\)-dimensional dynamical system with zero-dimensional set of periodic points can be covered by a metric zero-dimensional dynamical system via an at most \(2^n\)-to-one closed map. They are also concerned with periodic dynamical systems.