Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces

Dani, S. G. ; Margulis, G. A. (1991) Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 101 (1). pp. 1-17. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/101/1/1-17/...

Related URL: http://dx.doi.org/10.1007/BF02872005

Abstract

We show that ifG is a semisimple algebraic group defined overQ and Gamma is an arithmetic lattice inG:=G R with respect to theQ-structure, then there exists a compact subsetC ofG/Gamma such that, for any unipotent one-parameter subgroup {u t} ofG and anygε G, the time spent inC by the {u t}-trajectory ofgGamma, 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].

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Homogeneous Spaces; Unipotent Flows; Trajectories
ID Code:8216
Deposited On:26 Oct 2010 12:10
Last Modified:16 May 2016 18:16

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