Distribution of orbits of geometrically finite groups acting on null vectors

Nattalie Tamam; Jacqueline M. Warren

doi:10.1007/s10711-021-00669-0

Distribution of orbits of geometrically finite groups acting on null vectors

Nattalie Tamam, Jacqueline M. Warren^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We study the distribution of non-discrete orbits of geometrically finite groups in SO (n, 1) acting on Rⁿ⁺¹, and more generally on the quotient of SO (n, 1) by a horospherical subgroup. Using equidistribution of horospherical flows, we obtain both asymptotics for the distribution of orbits for the action of general geometrically finite groups, and we obtain quantitative statements with additional assumptions.

Original language	English
Article number	12
Journal	Geometriae Dedicata
Volume	216
Issue number	1
DOIs	https://doi.org/10.1007/s10711-021-00669-0
State	Published - Feb 2022
Externally published	Yes

Keywords

Discrete subgroups of Lie groups
Ergodic theory
Flows in homogeneous spaces
Homogeneous dynamics

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10.1007/s10711-021-00669-0

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AB - We study the distribution of non-discrete orbits of geometrically finite groups in SO (n, 1) acting on Rn+1, and more generally on the quotient of SO (n, 1) by a horospherical subgroup. Using equidistribution of horospherical flows, we obtain both asymptotics for the distribution of orbits for the action of general geometrically finite groups, and we obtain quantitative statements with additional assumptions.

KW - Discrete subgroups of Lie groups

KW - Ergodic theory

KW - Flows in homogeneous spaces

KW - Homogeneous dynamics

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Distribution of orbits of geometrically finite groups acting on null vectors

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