发散对角轨道平移的极限分布
动力系统
2019-08-15 v4
摘要
我们在齐次空间上局部有限测度（模缩放的等价类）的集合上定义了一种自然拓扑，并证明在此拓扑下，某些无限体积轨道的推前测度在周围空间中均匀分配。作为我们结果的应用，我们证明了当半径趋于无穷时，某些簇上球内整点个数的渐近公式。
引用
@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}
}
备注
A few arguments, notations and explanations are revised; several references are updated; to appear in Compositio Mathematica