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Journal of Fractal Geometry


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Volume 6, Issue 4, 2019, pp. 343–366
DOI: 10.4171/JFG/80

Published online: 2019-09-30

The case of equality in the dichotomy of Mohammadi–Oh

Laurent Dufloux[1]

(1) University of Jyväskylä, Finland

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.

Keywords: Bowen–Margulis–Sullivan measure, Burger–Roblin measure, ergodic geometry, ergodicity, recurrence, Besicovitch projection theorem

Dufloux Laurent: The case of equality in the dichotomy of Mohammadi–Oh. J. Fractal Geom. 6 (2019), 343-366. doi: 10.4171/JFG/80