Ergodicity of Unipotent Flows and Kleinian Groups

نویسنده

  • AMIR MOHAMMADI
چکیده

Let M be a non-elementary convex cocompact hyperbolic 3-manifold and δ be the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure if and only if δ > 1.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Invariant Radon Measures for Unipotent Flows and Products of Kleinian Groups

Let G = PSL2(F) where F = R,C, and consider the space Z = (Γ1 × Γ2)\(G × G) where Γ1 < G is a co-compact lattice and Γ2 < G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint [2] gives a classification of all ergodic invariant Radon measures on Z for the diagonal G-action. In this paper, for a horospherical subgroup N of G, we classify all ergodic, conservative, ...

متن کامل

On the space of ergodic invariant measures of unipotent flows

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

متن کامل

Unipotent flows on the space of branched covers of Veech surfaces

There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup U = {( 1 ∗ 0 1 )} . We classify the U -invariant ergodic measures on certain special submanifolds of the moduli space. (Each submanifold is the SL(2,R)-orbit of the set of branched covers of a fixed Veech surface.) For the U -action on these submanifolds, this is...

متن کامل

Unipotent Flows on Products of Sl(2,k)/γ’s

We will give a simplified and a direct proof of a special case of Ratner’s theorem on closures and uniform distribution of individual orbits of unipotent flows; namely, the case of orbits of the diagonally embedded unipotent subgroup acting on SL(2, K)/Γ1 × · · ·×SL(2, K)/Γn, where K is a locally compact field of characteristic 0 and each Γi is a cocompact discrete subgroup of SL(2, K). This sp...

متن کامل

Nondivergence of Horocyclic Flows on Moduli Space

The earthquake flow and the Teichmüller horocycle flow are flows on bundles over the Riemann moduli space of a surface, and are similar in many respects to unipotent flows on homogeneous spaces of Lie groups. In analogy with results of Margulis, Dani and others in the homogeneous space setting, we prove strong nondivergence results for these flows. This extends previous work of Veech. As coroll...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014