Genus one Birkhoff sections for geodesic flows on orbifolds

Pierre Dehornoy

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arXiv · 2603.23000

Genus one Birkhoff sections for geodesic flows on orbifolds

Pierre Dehornoy

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Abstract

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.

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BibTeX RIS

Pierre Dehornoy. 2026-03-24. Genus one Birkhoff sections for geodesic flows on orbifolds. https://arxiv.org/abs/2603.23000

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