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Article Dans Une Revue Duke Mathematical Journal Année : 2019

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

Résumé

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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Dates et versions

hal-01455739 , version 1 (03-02-2017)
hal-01455739 , version 2 (02-05-2017)

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François Maucourant, Barbara Schapira. On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds. Duke Mathematical Journal, 2019, 168 (4), pp.697-747. ⟨10.1215/00127094-2018-0050⟩. ⟨hal-01455739v2⟩
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