Measure Rigidity for Horospherical Subgroups of Groups Acting on Trees

Vladimir Finkelshtein, Cagri Sert*, Corina-Gabriela Ciobotaru

*Corresponding author af dette arbejde

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Abstract

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.

OriginalsprogEngelsk
TidsskriftInternational Mathematics Research Notices
Vol/bind2021
Nummer21
Sider (fra-til)16227-16270
Antal sider44
ISSN1073-7928
DOI
StatusUdgivet - nov. 2021
Udgivet eksterntJa

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