On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds

Abstract

We study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologi-cally 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 codi-mension of the unipotent flow inside the maximal unipotent flow. The latter result generalises a Theorem of Mohammadi and Oh.

References in corpus (1)

• A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds

Cited by in corpus (1)

• Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends