M变换中的n阶循环群判定  

Determing the Cyclic Group of Order n in Mbius Transformation

作　　者：甘欣荣[1] 钟寿国[2] 

机构地区：[1]武汉科技大学理学院,湖北武汉430065 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《郑州大学学报（理学版）》2012年第3期22-25,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：湖北省教育厅科研计划重点项目;编号D20111110

摘　　要：用二阶方阵的幂运算取代Mbius变换的迭代运算,借助2个常数Δ和δ以及2个与Δ,δ相关的数列Δn,δn,证明了任何二阶方阵n次幂后的4个元素均可用Δn,δn来表达.进而得到M变换为n阶循环群的判定式.By replacing iterative computation in Mbius transformation（MT） with computation of powers of 2×2 square matrix,and by using two constants Δ and δ as well as two seguences Δn,δn related to Δ,δ,a formula of the nth of a 2×2 square matrix was proved in terms of Δn and δn,and a criterion of MT being a cyclic group of order n was given.

关 键 词：Mbius变换 方阵 循环映射 

分 类 号：O152.1[理学—数学] O152.3[理学—基础数学]