有限性猜想在SL(2,Z>=0)^2中成立
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2021-08-11 v2 数值分析
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数值分析
摘要
设A、B为SL(2,R)中迹大于等于2的矩阵。假设矩阵对A、B是协调定向的，即可以共轭为一对具有非负元素的矩阵。还假设要么A、B^(-1)也是协调定向的，要么A、B具有整数元素。则Lagarias-Wang有限性猜想对集合{A,B}成立，其最优乘积在{A,B,AB,A^2B,AB^2}中。特别地，它对SL(2,Z>=0)中的每个矩阵对都成立。
引用
@article{arxiv.2006.16899,
title = {The finiteness conjecture holds in SL(2,Z>=0)^2},
author = {Giovanni Panti and Davide Sclosa},
journal= {arXiv preprint arXiv:2006.16899},
year = {2021}
}
备注
To appear in Nonlinearity; we sincerely thank the referee for the precious remarks. The ArXiv version is outdated, but we cannot replace it due to copyright reasons. The final author-created, un-copyedited version of this paper is available from the first author's home page