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 R-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions R→ [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).

Original languageEnglish
Pages (from-to)81-91
Number of pages11
JournalJournal of Dynamics and Differential Equations
Volume31
Issue number1
DOIs
Publication statusPublished - Mar 15 2019

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