Séminaire Géométrie et groupes discrets

Dynamics of Unipotent Frame Flows for Hyperbolic Manifolds

by Prof. Barbara Schapira (Université de Rennes 1)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

In joint work with François Maucourant, we study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologically transitive, and that the natural invariant measure, the so-called "Burger-Roblin measure", is ergodic, as soon as the geodesic flow admits a finite measure of maximal entropy, and this entropy is strictly greater than the codimension of the unipotent flow inside the maximal unipotent flow. The latter result generalises a theorem of Mohammadi and Oh.

In the talk, I will present the main ideas of this work.

Organized by

Fanny Kassel