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

## TL;DR

This paper investigates the dynamics of unipotent flows on frame bundles of hyperbolic manifolds with infinite volume, establishing topological transitivity and ergodicity of the Burger-Roblin measure under certain entropy conditions.

## Contribution

It generalizes a theorem of Mohammadi and Oh by proving ergodicity of the Burger-Roblin measure for a broader class of hyperbolic manifolds.

## Key findings

- Unipotent flows are topologically transitive.
- The Burger-Roblin measure is ergodic under specified entropy conditions.
- Results extend previous theorems to infinite volume 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.