Mathematics > Dynamical Systems
[Submitted on 31 Mar 2018 (v1), last revised 26 Sep 2018 (this version, v3)]
Title:Limiting distribution of translates of the orbit of a maximal $\mathbb{Q}$-torus from identity on $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$
View PDFAbstract:Given a maximal $\mathbb{Q}$-torus in $SL(N,\mathbb{Q})$, its orbit from identity coset in $SL(N,\mathbb{R})/SL(N,\mathbb{Z})$ naturally carries a possibly infinite Haar measure. We classify all possible limit measures of it when translated by a sequence of elements from $SL(N,\mathbb{R})$. This is a natural extension of Shapira and Zheng's work where only $\mathbb{Q}$-split tori are considered.
Submission history
From: Runlin Zhang [view email][v1] Sat, 31 Mar 2018 23:30:08 UTC (34 KB)
[v2] Mon, 16 Apr 2018 15:05:02 UTC (35 KB)
[v3] Wed, 26 Sep 2018 01:10:01 UTC (42 KB)
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