Universality with respect to image-limit sets Original Research Article

A discrete dynamical system on a compact metric space XX is called universal (with respect to ωω-limit sets) if, among its ωω-limit sets, there is a homeomorphic copy of any ωω-limit set of any dynamical system on XX. 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.