Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913368713986048 |
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| author | Einabadi, Nastaran |
| author_facet | Einabadi, Nastaran |
| contents | We prove that a generic element of the Anosov-Katok class of the torus, $\overline{\mathcal{O}}^{\infty}(\mathbb{T}^2)$, acts parabolically and non-properly on the fine curve graph $C^{\dagger}(\mathbb{T}^2)$. Additionally, we show that a generic element of $\overline{\mathcal{O}}^{\infty}(\mathbb{T}^2)$ admits generalized rotation sets of any point-symmetric compact convex homothety type in the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets Einabadi, Nastaran Dynamical Systems Group Theory Geometric Topology We prove that a generic element of the Anosov-Katok class of the torus, $\overline{\mathcal{O}}^{\infty}(\mathbb{T}^2)$, acts parabolically and non-properly on the fine curve graph $C^{\dagger}(\mathbb{T}^2)$. Additionally, we show that a generic element of $\overline{\mathcal{O}}^{\infty}(\mathbb{T}^2)$ admits generalized rotation sets of any point-symmetric compact convex homothety type in the plane. |
| title | Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets |
| topic | Dynamical Systems Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2405.19123 |