TY - JOUR
T1 - Measure Rigidity for Horospherical Subgroups of Groups Acting on Trees
AU - Finkelshtein, Vladimir
AU - Sert, Cagri
AU - Ciobotaru, Corina-Gabriela
N1 - Publisher Copyright:
© 2019 The Author(s) 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
PY - 2021/11
Y1 - 2021/11
N2 - We prove analogues of some of the classical results in homogeneous dynamics in nonlinear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma \leq G$ a discrete subgroup. For a large class of groups $G$, we give a classification of the probability measures on $G/\Gamma $ invariant under horospherical subgroups. When $\Gamma $ is a cocompact lattice, we show the unique ergodicity of the horospherical action. We prove Hedlund's theorem for geometrically finite quotients. Finally, we show equidistribution of large compact orbits.
AB - We prove analogues of some of the classical results in homogeneous dynamics in nonlinear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma \leq G$ a discrete subgroup. For a large class of groups $G$, we give a classification of the probability measures on $G/\Gamma $ invariant under horospherical subgroups. When $\Gamma $ is a cocompact lattice, we show the unique ergodicity of the horospherical action. We prove Hedlund's theorem for geometrically finite quotients. Finally, we show equidistribution of large compact orbits.
UR - http://www.scopus.com/inward/record.url?scp=85122198338&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnz275
DO - 10.1093/imrn/rnz275
M3 - Journal article
AN - SCOPUS:85122198338
SN - 1073-7928
VL - 2021
SP - 16227
EP - 16270
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 21
ER -