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SL(2,Qp)中的非初等离散子群的代数收敛性
杨静桦
作者单位E-mail
杨静桦 上海大学 理学院, 上海 200444 davidyoung@amss.ac.cn 
摘要:
在Kleinian群中,研究离散群的代数收敛性是一个重要的问题,群列的代数收敛性与流形的形变以及极限集的Hausdorff维数的收敛性有密切关系.随着非阿基米德域上的李群和非阿基米德域上的动力系统的发展,讨论非阿基米德域上的离散群的代数收敛性就是一个重要的问题.这篇文章讨论了PSL(2,Qp)中由r个元素生成的非初等离散群的代数收敛性,利用PSL(2,Qp)中关于子群的非阿基米德Jorgensen不等式,以及群双曲Berkovich空间上的双曲等距性,证明了非初等群列代数收敛到非初等群列上.
关键词:  p-adic Mobius变换  代数收敛性  离散群
DOI:10.3969/J.ISSN.100-5137.2017.03.003
分类号:
基金项目:This research was supported by Natural Science Foundation of China (11301510, 11671092)
On algebraic convergence of non-elementary discrete subgroups of SL(2,Qp)
Yang Jinghua
Abstract:
In the Kelinian groups, the study of the algebraic convergence of the sequence of the discrete subgroups is a very important topic, since the algebraic convergence of the sequence of the discrete subgroups can be applied to study the deformations the manifolds and the Hausdorff dimension of the limit sets of the discrete subgroups. With the rapid developments of the p-adic Lie groups and the algebraic dynamical systems, it is very important to study the topics of algebraic convergence of the p-adic discrete subgroups. In this paper, we discuss the algebraic convergence of a sequence {Gn,r} of r-generator non-elementary discretesubgroups of PSL(2,Qp) by use of the Jorgensen inequalities in PSL(2,Qp) and the subgroups of PSL(2,Qp) acting isometrically on the hyperbolic Berkovich space. We prove that a sequence {Gn,r} of r-generator non-elementary discretesubgroups of PSL(2,Qp) converges to a non-elementary discrete subgroup of PSL(2,Qp) algebraically.
Key words:  p-adic Mobius maps  algebraic convergence  discrete subgroups