Genus one Birkhoff sections for geodesic flows on orbifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914417433640960 |
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| author | Dehornoy, Pierre |
| author_facet | Dehornoy, Pierre |
| contents | For $\mathcal{O}$ a hyperbolic orientable 2-orbifold of genus $g$ with at most $2g+6$ conic points, we prove that the geodesic flow on the unitary tangent bundle$\mathrm{T}^1\mathcal{O}$ admits a Birkhoff section whose genus is one. Together with a result of Minakawa, this implies that this flow is almost equivalent to the suspension flow of the $(\begin{smallmatrix}2\&1\\1\&1\end{smallmatrix})$-map on the torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Genus one Birkhoff sections for geodesic flows on orbifolds Dehornoy, Pierre Dynamical Systems Geometric Topology For $\mathcal{O}$ a hyperbolic orientable 2-orbifold of genus $g$ with at most $2g+6$ conic points, we prove that the geodesic flow on the unitary tangent bundle$\mathrm{T}^1\mathcal{O}$ admits a Birkhoff section whose genus is one. Together with a result of Minakawa, this implies that this flow is almost equivalent to the suspension flow of the $(\begin{smallmatrix}2\&1\\1\&1\end{smallmatrix})$-map on the torus. |
| title | Genus one Birkhoff sections for geodesic flows on orbifolds |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2603.23000 |