Genus one Birkhoff sections for geodesic flows on orbifolds
Dynamical Systems
2026-03-25 v1 Geometric Topology
Abstract
For a hyperbolic orientable 2-orbifold of genus with at most conic points, we prove that the geodesic flow on the unitary tangent bundle 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 -map on the torus.
Cite
@article{arxiv.2603.23000,
title = {Genus one Birkhoff sections for geodesic flows on orbifolds},
author = {Pierre Dehornoy},
journal= {arXiv preprint arXiv:2603.23000},
year = {2026}
}