On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds
Dynamical Systems
2019-05-29 v2
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.
Keywords
Cite
@article{arxiv.1702.01689,
title = {On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds},
author = {François Maucourant and Barbara Schapira},
journal= {arXiv preprint arXiv:1702.01689},
year = {2019}
}