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Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics

Published online by Cambridge University Press:  02 May 2017

RODOLPHE RICHARD  and
NIMISH A. SHAH Open the ORCID record for NIMISH A. SHAH [Opens in a new window]
RODOLPHE RICHARD
Affiliation:
University College London, London WC1E 6BT, UK email Rodolphe.RICHARD@Normalesup.org
NIMISH A. SHAH
Affiliation:
The Ohio State University, Columbus, OH 43210, USA email shah@math.ohio-state.edu
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Abstract

Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and linearization techniques, in view of Ratner’s measure classification for unipotent flows, reduce such problems to dynamical questions about linear actions of reductive groups on finite-dimensional vector spaces. This article provides general results which resolve these linear dynamical questions in terms of natural group theoretic or geometric conditions.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 7 , October 2018 , pp. 2780 - 2800
Copyright
© Cambridge University Press, 2017 

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