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arXiv · 2510.08706

A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem

Yonatan Gutman·Qiang Huo·Masaki Tsukamoto
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Abstract

We prove that a continuous action of $\mathbb{R}^n$ on a compact metrizable space equivariantly embeds into the shift action on the space of one-Lipschitz functions from $\mathbb{R}^n$ to $[0,1]$ if and only if the set of fixed points topologically embeds in $[0,1]$. This is a Lipschitz refinement of classical dynamical embedding theorems of Bebutov, Kakutani, Jaworski and Chen.

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Yonatan Gutman, Qiang Huo, Masaki Tsukamoto. 2025-10-09. A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem. https://arxiv.org/abs/2510.08706

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