Coding of geodesics and Lorenz-like templates for some geodesic flows

Pierre Dehornoy (1) , Tali Pinsky (2)

1 IF - Institut Fourier
2 British Columbia

We construct a template with two ribbons that describes the topology of all periodic orbits of the geodesic flow on the unit tangent bundle to any sphere with three cone points with hyperbolic metric. The construction relies on the existence of a particular coding with two letters for the geodesics on these orbifolds.

Mots clés: Geodesic; Knot; Flow; Template

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

Pierre Dehornoy, Tali Pinsky. Coding of geodesics and Lorenz-like templates for some geodesic flows. Ergodic Theory and Dynamical Systems, 2018, 38 (3), ⟨10.1017/etds.2016.59⟩. ⟨hal-01083278v2⟩