0000000000026225

AUTHOR

Laurent Dufloux

showing 2 related works from this author

The case of equality in the dichotomy of Mohammadi–Oh

2019

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.

CombinatoricsMathematics::Group TheoryIntegerDiscrete groupGroup (mathematics)Astrophysics::High Energy Astrophysical PhenomenaApplied MathematicsErgodicityGeometry and TopologyMeasure (mathematics)Frame bundleQuotientMathematicsJournal of Fractal Geometry
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The case of equality in the dichotomy of Mohammadi-Oh

2017

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.

ergodic geometryMathematics::Group TheoryrecurrenceBurger-Roblin measure37C45 28A80 53D25 37D40Bowen-Margulis-Sullivan measureBesicovitch projection theoremAstrophysics::High Energy Astrophysical PhenomenaFOS: MathematicsergodicitygeometriaDynamical Systems (math.DS)Mathematics - Dynamical Systems
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