Ping-pong dynamics of hyperbolic-like actions with non-simple points
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912409523847168 |
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| author | Kim, KyeongRo Triestino, Michele |
| author_facet | Kim, KyeongRo Triestino, Michele |
| contents | A hyperbolic-like group is a subgroup of $\operatorname{Homeo}_+(S^1)$ such that every non-trivial element has exactly two fixed points, one attracting and one repelling. We investigate the ping-pong dynamics of hyperbolic-like groups, inspired by a conjecture of Bonatti. We show the existence of a proper ping-pong partition for any pair of non-cyclic point stabilizers. More precisely, our results explicitly provide such a ping-pong partition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ping-pong dynamics of hyperbolic-like actions with non-simple points Kim, KyeongRo Triestino, Michele Geometric Topology Dynamical Systems Group Theory Primary: 57M60, Secondary: 37C85, 37B05 A hyperbolic-like group is a subgroup of $\operatorname{Homeo}_+(S^1)$ such that every non-trivial element has exactly two fixed points, one attracting and one repelling. We investigate the ping-pong dynamics of hyperbolic-like groups, inspired by a conjecture of Bonatti. We show the existence of a proper ping-pong partition for any pair of non-cyclic point stabilizers. More precisely, our results explicitly provide such a ping-pong partition. |
| title | Ping-pong dynamics of hyperbolic-like actions with non-simple points |
| topic | Geometric Topology Dynamical Systems Group Theory Primary: 57M60, Secondary: 37C85, 37B05 |
| url | https://arxiv.org/abs/2506.01690 |