Universality with respect to -limit sets

Abstract: A discrete dynamical system on a compact metric space is called universal (with respect to -limit sets) if, among its -limit sets, there is a homeomorphic copy of any -limit set of any dynamical system on . 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. [Copyright &y& Elsevier]