SL(2,Q_p)中的非初等离散子群的代数收敛性（英文）  

On algebraic convergence of non-elementary discrete subgroups of SL(2,Q_p)

作　　者：杨静桦[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海师范大学学报（自然科学版）》2017年第3期358-362,共5页Journal of Shanghai Normal University(Natural Sciences)

基　　金：supported by Natural Science Foundation of China(11301510,11671092)

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.讨论了PSL(2,Q_p)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,Q_p)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.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 sub-groups 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 dis-crete 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.

关 键 词：p-adicMobius变换 代数收敛性 离散群 

分 类 号：O174.51[理学—数学]