Projections of Patterson-Sullivan measures and the dichotomy of Mohammadi-Oh
Dufloux, Laurent (2017-11-30)
Dufloux, L. Isr. J. Math. (2018) 223: 399. https://doi.org/10.1007/s11856-017-1622-8
© Hebrew University of Jerusalem 2018. This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-017-1622-8.
Let Γ be some discrete subgroup of SO°(n + 1, R) with finite Bowen-Margulis-Sullivan measure. We study the dynamics of the Bowen-Margulis-Sullivan measure with respect to closed connected subspaces of the N component in some Iwasawa decomposition SO°(n+1, R) = KAN. We also study the dimension of projected Patterson-Sullivan measures along some fixed direction.
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