Limiting Distributions of Translates of Divergent Diagonal Orbits
Dynamical Systems
2019-08-15 v4
Abstract
We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the ambient space. As an application of our results we prove an asymptotic formula for the number of integral points in a ball on some varieties as the radius goes to infinity.
Keywords
Cite
@article{arxiv.1712.00630,
title = {Limiting Distributions of Translates of Divergent Diagonal Orbits},
author = {Uri Shapira and Cheng Zheng},
journal= {arXiv preprint arXiv:1712.00630},
year = {2019}
}
Comments
A few arguments, notations and explanations are revised; several references are updated; to appear in Compositio Mathematica