Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909229658406912 |
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| author | Malicet, Dominique Militon, Emmanuel |
| author_facet | Malicet, Dominique Militon, Emmanuel |
| contents | In 2000, Margulis proved that any group of homeomorphisms of the circle either preserves a probabilty measure on the circle or contains a free subgroup in two generators, which is reminiscent of the Tits alternatve for linear groups. In this article, we prove an analogous statement for groups of locally monotonic homeomorphisms of a compact subset of R. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08070 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative Malicet, Dominique Militon, Emmanuel Dynamical Systems Group Theory Geometric Topology In 2000, Margulis proved that any group of homeomorphisms of the circle either preserves a probabilty measure on the circle or contains a free subgroup in two generators, which is reminiscent of the Tits alternatve for linear groups. In this article, we prove an analogous statement for groups of locally monotonic homeomorphisms of a compact subset of R. |
| title | Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative |
| topic | Dynamical Systems Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2304.08070 |