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PreprintarXiv licencearXiv

A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions

  • Yonatan Gutman
  • Qiang Huo
  • Kangbo Ouyang
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Abstract

Let G be a connected Lie group equipped with a compatible right-invariant metric and let G act continuously on a compact metrizable space X. We prove that X admits a G-equivariant embedding into the right argument shift action on the space of one-Lipschitz maps from G to [0,1] if and only if the set of fixed points topologically embeds into [0,1]. This generalizes a theorem proved by Gutman, Huo and Tsukamoto for ℝk-flows.

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Cite

BibTeXRIS
BibTeX
@misc{gutman2026lipschitz,
  title = {{A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions}},
  author = {Yonatan Gutman and Qiang Huo and Kangbo Ouyang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13091},
  eprint = {2610.13091},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13091},
}
RIS
TY  - UNPB
TI  - A Lipschitz refinement of the Bebutov-Kakutani dynamical embedding theorem for connected Lie group actions
AU  - Yonatan Gutman
AU  - Qiang Huo
AU  - Kangbo Ouyang
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13091
UR  - https://arxiv.org/abs/2610.13091
AB  - Let G be a connected Lie group equipped with a compatible right-invariant metric and let G act continuously on a compact metrizable space X. We prove that X admits a G-equivariant embedding into the right argument shift action on the space of one-Lipschitz maps from G to [0,1] if and only if the set of fixed points topologically embeds into [0,1]. This generalizes a theorem proved by Gutman, Huo and Tsukamoto for ℝ^k-flows.
ER  -