Journal ArticleDOI
Distribution of orbits in ℝ 2 of a finitely generated group of SL(2,ℝ)
TLDR
In this article, the asymptotic distribution of the non-discrete orbits of a finitely generated group acting linearly on the unitary tangent bundle of the associated surface was studied.Abstract:
In this work, we study the asymptotic distribution of the non-discrete orbits of a finitely
generated group acting linearly on ${\Bbb R}^2$. To do this, we establish new equidistribution
results for the horocyclic flow on the unitary tangent bundle of the associated surface.read more
Citations
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Journal ArticleDOI
Classification of joinings for Kleinian groups
Amir H. Mohammadi,Hee Oh +1 more
TL;DR: In this article, all locally finite joinings of a horospherical subgroup action on Γ ∖G when Γ is a Zariski-dense geometrically finite subgroup of G = PSL2(R) or PSL 2(C) were studied.
Posted Content
On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold
TL;DR: In this paper, it was shown that the Radon-Nikodym cocycle of the leaves of the horospherical foliation is uniquely determined by a Gibbs measure on a convex-cocompact negatively curved manifold.
Journal ArticleDOI
Classification of joinings for Kleinian groups
Amir H. Mohammadi,Hee Oh +1 more
TL;DR: In this article, all locally finite joinings of a horospherical subgroup action on Gamma G when G is a Zariski dense geometrically finite subgroup of G = PSL_2(R) or PSL-2(C).
Journal ArticleDOI
A short proof of unique ergodicity of horospherical foliations on infinite volume hyperbolic manifolds
TL;DR: In this paper, the authors give a short proof of the unique ergodicity of the strong stable foliation of the geodesic flow on the frame bundle of a hyperbolic manifold admitting a finite measure of maximal entropy.
Journal ArticleDOI
A universal divergence rate for symmetric Birkhoff Sums in infinite ergodic theory
TL;DR: In this paper, it was shown that there exists a universal gap in the failure of the ergodic theorem for symmetric Birkhoff sums in infinite ergodics theory, and an application of this result to a question of fluctuations of the Birhoff integrals of horocyclic flows on geometrically finite surfaces is given.
References
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Book
An introduction to infinite ergodic theory
TL;DR: In this article, the authors propose non-singular transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions Hyperbolic geodesic flows Cocycles and skew products Bibliography index.
Journal ArticleDOI
Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
Book
Ergodic Theory: with a view towards Number Theory
Manfred Einsiedler,Thomas Ward +1 more
TL;DR: In this article, Furstenberg's Proof of Szemeredi's Theorem has been used to prove the existence of locally compact groups on the Hyperbolic Plane for continuous maps.
BOOK REVIEW Ergodic Theory: with a view towards Number Theory
Manfred Einsiedler,Thomas Ward +1 more
TL;DR: Ergodic theory has had an intense influence on number theory as discussed by the authors, and the recent works of M. Einsiedler, A. Katok and E. Lindenstrauss on the Littlewood conjecture may be recalled as some of the dramatic episodes in successful applications in combinatorial number theory, diophantine approximation and other topics in number theory.
Journal ArticleDOI
Ergodicité et équidistribution en courbure négative
TL;DR: In this article, the authors consider a groupe d'isometries discret agissant sur un espace CAT(-1), nous etablissons successivement, par des methodes nouvelles et elementaires, un theoreme d'ergodicite du feuilletage horospherique associe, le melange du flot geodesique, l'equidistribution des points orbitaux du groupe, avec premier terme asymptotique exponentiel de la fonction orbitale,