Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 4 (2019), 697-747.
On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds
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.
Duke Math. J., Volume 168, Number 4 (2019), 697-747.
Received: 2 May 2017
Revised: 19 October 2018
First available in Project Euclid: 5 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 37C45: Dimension theory of dynamical systems 37A40: Nonsingular (and infinite-measure preserving) transformations 28D20: Entropy and other invariants 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Maucourant, François; Schapira, Barbara. On topological and measurable dynamics of unipotent frame flows for hyperbolic manifolds. Duke Math. J. 168 (2019), no. 4, 697--747. doi:10.1215/00127094-2018-0050. https://projecteuclid.org/euclid.dmj/1549392546