We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution result was first obtained in the early 1980s by Dani and Smillie [DS84] and later reappeared as an illustrative special case [Rat92] of Ratner’s work [Rat91-Rat94] on the equidistribution of unipot...

Understanding the limiting distributions of translates of measures on submanifolds of homogeneous spaces of Lie groups lead to very interesting number theoretic and geometric applications. We explore this theme in various generalities, and in specific cases. Our main tools are Ratner’s theorems on unipotent flows, nondivergence theorems of Dani and Margulis, and dynamics of linear actions of se...

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...

The Historical Journal / Volume 56 / Issue 03 / September 2013, pp 729 756 DOI: 10.1017/S0018246X1300023X, Published online: 05 August 2013 Link to this article: http://journals.cambridge.org/abstract_S0018246X1300023X How to cite this article: JEREMY NUTTALL (2013). PLURALISM, THE PEOPLE, AND TIME IN LABOUR PARTY HISTORY, 1931–1964. The Historical Journal, 56, pp 729-756 doi:10.1017/ S0018246X...

Abstract In the present work, a two-parameter empirical formula is proposed, based on Geiger-Nuttall law, to study two-proton ( ) radioactivity. Using this formula, calculated radioactivity half-lives are in good agreement with experimental data as well results obtained by Goncalves et al . [ Phys. Lett. B 774 , 14 (2017)] using effective liquid drop model (ELDM), Sreeja Eur. J...

this article is devoted to two theorems on tangent circles, which were discovered by the iranian geometer abu sah?l kuhi (fourth century h.). the two theorems were inspired by the book of lemmas (makhudhat) attributed to archimedes. kuh?'s original treatise is lost, but the two theorems are found in nas??r al-d? ntu?s?'s edition of the lemmas of archimedes. they then appeared in latin...

We consider the Teichmüller flow on the unit cotangent bundle of the moduli space of compact Riemann surfaces with punctures. We show that it is exponentially mixing for the Ratner class of observables. More generally, this result holds for the restriction of the Teichmüller flow to an arbitrary connected component of stratum. This result generalizes [AGY] which considered the case of strata of...

This paper continues the theme started in 1971 by G.A. Margulis [22] when he showed that trajectories of one-parameter unipotent flows on SL(k,R)/ SL(k,Z) are never divergent. This was earlier conjectured by I. Piatetski-Shapiro, and was used by Margulis for the proof of the Arithmeticity Theorem for non-uniform lattices. A decade later, S. G. Dani [7, 8, 10] modified the method of Margulis, sh...

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More precisely: Let G be a Lie group (not necessarily connected) and Γ a closed subgroup of G. Let W be a subgroup of G such that AdG(W ) is contained in the Zariski clos...