A “universal” dynamical system generated by a continuous map of the interval

Pokluda, David; Smítal, Jaroslav

doi:10.1090/S0002-9939-00-05679-3

A “universal” dynamical system generated by a continuous map of the interval
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by David Pokluda and Jaroslav Smítal PDF

Proc. Amer. Math. Soc. 128 (2000), 3047-3056 Request permission

Abstract:

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

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