Measure Rigidity for Horospherical Subgroups of Groups Acting on Trees
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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.
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2014 ◽
Vol 98
(3)
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pp. 390-406
2011 ◽
Vol 147
(4)
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pp. 1230-1280
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1996 ◽
Vol 120
(4)
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pp. 647-662
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