Genus one Birkhoff sections for geodesic flows on orbifolds

Fuente: arXiv
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Main Author: Dehornoy, Pierre
Format: Preprint
Published: 2026
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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