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arXiv · 1809.02039

A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem

Yonatan Gutman·Lei Jin·Masaki Tsukamoto
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Abstract

We prove that an $\mathbb{R}$-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions $\mathbb{R}\to[0,1]$ if its fixed point set can be topologically embedded in the unit interval. This is a refinement of the classical Bebutov--Kakutani theorem (1968).

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Yonatan Gutman, Lei Jin, Masaki Tsukamoto. 2018-09-06. A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem. https://doi.org/10.1007/s10884-018-9653-3

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