Groups of automorphisms of trees and their limit sets
1997 ◽
Vol 17
(4)
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pp. 869-884
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Keyword(s):
Let $T$ be a locally finite simplicial tree and let $\Gamma\subset{\rm Aut}(T)$ be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincaré series associated with $\Gamma$, which is also the Hausdorff dimension of the limit set of $\Gamma$; this uses a description due to Lubotzky of an appropriate fundamental domain for finite index torsion-free subgroups of $\Gamma$. Coornaert, generalizing work of Sullivan, showed that the limit set is of finite positive measure in its dimension; we give a new proof of this result. Finally, we show that the critical exponent is locally constant on the space of deformations of $\Gamma$.
Keyword(s):
2020 ◽
Vol 0
(0)
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2000 ◽
Vol 128
(1)
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pp. 123-139
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Keyword(s):
2009 ◽
Vol 147
(2)
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pp. 455-488
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2019 ◽
Vol 2019
(746)
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pp. 149-170
Keyword(s):
1995 ◽
Vol 06
(01)
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pp. 19-32
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Keyword(s):
2019 ◽
Vol 29
(03)
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pp. 603-614
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Keyword(s):
2011 ◽
Vol 21
(11)
◽
pp. 3205-3215
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Keyword(s):