A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912640264044544 |
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| author | Gutman, Yonatan Huo, Qiang Tsukamoto, Masaki |
| author_facet | Gutman, Yonatan Huo, Qiang Tsukamoto, Masaki |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem Gutman, Yonatan Huo, Qiang Tsukamoto, Masaki Dynamical Systems 37B02, 37B05 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. |
| title | A Lipschitz Refinement of the Multidimensional Bebutov--Kakutani Dynamical Embedding Theorem |
| topic | Dynamical Systems 37B02, 37B05 |
| url | https://arxiv.org/abs/2510.08706 |