Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces |
| |
Authors: | S G Dani G A Margulis |
| |
Institution: | 1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Bombay, India 2. Institute for Problems of Information Transmission, ul. Ermolovoi 19, 101 447, Moscow, USSR
|
| |
Abstract: | We show that ifG is a semisimple algebraic group defined overQ and Γ is an arithmetic lattice inG:=G
R with respect to theQ-structure, then there exists a compact subsetC ofG/Γ such that, for any unipotent one-parameter subgroup {u
t} ofG and anyg∈G, the time spent inC by the {u
t}-trajectory ofgΓ, during the time interval 0,T], is asymptotic toT, unless {g
−1utg} is contained in aQ-parabolic subgroup ofG. Some quantitative versions of this are also proved. The results strengthen similar assertions forSL(n,Z),n≥2, proved earlier in 5] and also enable verification of a technical condition introduced in 7] for lattices inSL(3,R), which was used in our proof of Raghunathan’s conjecture for a class of unipotent flows, in 8]. |
| |
Keywords: | Homogeneous spaces unipotent flows trajectories |
本文献已被 SpringerLink 等数据库收录! |
|