A ``universal'' dynamical system generated by a continuous map of the interval

Abstract

In this paper we show that there is a continuous map f : I → I of the interval such that any ω-limit set W of any continuous map g : I → I can be transformed by a homeomorphism I → I to an ω-limit set W of f . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an ω-limit set of f .