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. Ergodic Theory and Dynamical Systems, 2015, 35 (6), pp.1795-1813. ⟨10.1017/etds.2014.14⟩. ⟨hal-00725790v2⟩