Universality with respect to [formula omitted]-limit sets

Abstract

A discrete dynamical system on a compact metric space X is called universal (with respect to ω -limit sets) if, among its ω -limit sets, there is a homeomorphic copy of any ω -limit set of any dynamical system on X . By a result of Pokluda and Smítal the unit interval admits a universal system. In this paper, we study the problem of the existence of universal systems on Cantor spaces, graphs, dendrites and higher-dimensional spaces.