Checking ergodicity of some geodesic flows with infinite Gibbs measure
1981 ◽
Vol 1
(1)
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pp. 107-133
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Keyword(s):
AbstractThis paper concerns a problem which arose from a paper of Sullivan. Let Γ be a discrete group of isometries of hyperbolic space Hd+1. We study the question of when the geodesic flow on the unit tangent bundle UT (Hd+1/Γ) of Hd+1/Γ is ergodic with respect to certain natural measures. As a consequence, we study the question of when Γ is of divergence type. Ergodicity when the non-wandering set of UT (Hd+1/Γ) is compact is already known from the theory of symbolic dynamics, due to Bowen, or from Sullivan's work. For such a Γ, we consider a subgroup Γ1 of Γ with Γ/Γ1 ≅ℤυ and prove the geodesic flow on UT (Hd+1/Γ1) is ergodic (with respect to one of these natural measures) if and only if υ ≤ 2.
Keyword(s):
1991 ◽
Vol 11
(4)
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pp. 653-686
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2014 ◽
Vol 35
(6)
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pp. 1795-1813
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Keyword(s):
1997 ◽
Vol 17
(1)
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pp. 211-225
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1983 ◽
Vol 3
(1)
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pp. 1-12
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Keyword(s):
1982 ◽
Vol 2
(3-4)
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pp. 513-524
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Keyword(s):
1993 ◽
Vol 13
(2)
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pp. 335-347
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