Orbital equivalence classes of finite coverings of geodesic flows

Classes d'équivalences orbitales de relevés de flots géodésiques

Thierry Barbot (1) , Sérgio Fenley (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 FSU - Florida State University [Tallahassee]

Let $M$ be a closed 3-manifold admitting a finite cover of index n along the fibers over the unit tangent bundle of a closed surface. We prove that if n is odd, there is only one Anosov flow on M up to orbital equivalence, and if n is even, there are two orbital equivalence classes of Anosov flows on M.

Keywords: Anosov flows; geodesic flow; mapping class group

Domains: Dynamical Systems [math.DS]; Geometric Topology [math.GT]

Thierry Barbot, Sérgio Fenley. Orbital equivalence classes of finite coverings of geodesic flows: Orbital equivalence classes of finite coverings of geodesic flows. 2024. ⟨hal-03657558v2⟩