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15 March 2019 On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds
François Maucourant, Barbara Schapira
Duke Math. J. 168(4): 697-747 (15 March 2019). DOI: 10.1215/00127094-2018-0050

Abstract

We study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologically 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 codimension of the unipotent flow inside the maximal unipotent flow. The latter result generalizes a theorem of Mohammadi and Oh.

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François Maucourant. Barbara Schapira. "On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds." Duke Math. J. 168 (4) 697 - 747, 15 March 2019. https://doi.org/10.1215/00127094-2018-0050

Information

Received: 2 May 2017; Revised: 19 October 2018; Published: 15 March 2019
First available in Project Euclid: 5 February 2019

zbMATH: 07055153
MathSciNet: MR3916066
Digital Object Identifier: 10.1215/00127094-2018-0050

Subjects:
Primary: 37D40
Secondary: 20H10 , 22E40 , 28D20 , 37A40 , 37C45

Keywords: Bowen–Margulis–Sullivan measure , Burger–Roblin measure , ergodicity , frame flows , Marstrand’s theorem , Mixing , unipotent flows

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 4 • 15 March 2019
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