Genus one Birkhoff sections for geodesic flows

Pierre Dehornoy (1)

1 Mathematisches Institut [Bern]

We prove that the geodesic flow on the unit tangent bundle to every hyperbolic 2-orbifold that is a sphere with 3 or 4 singular points admits explicit genus one Birkhoff sections, and we determine the associated first return maps.

Mots clés: cross section; geodesic flow; suspension flow

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Pierre Dehornoy. Genus one Birkhoff sections for geodesic flows. 2012. ⟨hal-00725790v1⟩