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PreprintCC BY 4.0arXiv

Non-determinism in group actions and topological minimal self-joinings

  • Nicolás Bitar
  • Sebastián Donoso
  • Samuel Petite
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Abstract

We study the topological and geometrical aspects of non-determinism in group actions, generalizing the notion of non-expansive direction for abelian actions. Under suitable conditions on the acting group, we establish restrictions on the collection of non-deterministic horoballs (or half-spaces) for any action. We illustrate our results in the case of free and nilpotent groups, expanding upon known cases for abelian groups. We then apply these findings to standing problems concerning minimal self-joinings in topological dynamics, which are of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{bitar2026nondeterminism,
  title = {{Non-determinism in group actions and topological minimal self-joinings}},
  author = {Nicolás Bitar and Sebastián Donoso and Samuel Petite},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26479},
  eprint = {2609.26479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26479},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-determinism in group actions and topological minimal self-joinings
AU  - Nicolás Bitar
AU  - Sebastián Donoso
AU  - Samuel Petite
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26479
UR  - https://arxiv.org/abs/2609.26479
AB  - We study the topological and geometrical aspects of non-determinism in group actions, generalizing the notion of non-expansive direction for abelian actions. Under suitable conditions on the acting group, we establish restrictions on the collection of non-deterministic horoballs (or half-spaces) for any action. We illustrate our results in the case of free and nilpotent groups, expanding upon known cases for abelian groups. We then apply these findings to standing problems concerning minimal self-joinings in topological dynamics, which are of independent interest.
ER  -