A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

Yonatan Gutman; Lei Jin; Masaki Tsukamoto

doi:10.1007/s10884-018-9653-3

A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem

Yonatan Gutman, Lei Jin, Masaki Tsukamoto

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	81-91
Number of pages	11
Journal	Journal of Dynamics and Differential Equations
Volume	31
Issue number	1
DOIs	https://doi.org/10.1007/s10884-018-9653-3
Publication status	Published - Mar 15 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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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).",

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