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arXiv · 1702.01689

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

François Maucourant·Barbara Schapira
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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.

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François Maucourant, Barbara Schapira. 2017-05-02. On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds. https://doi.org/10.1215/00127094-2018-0050

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