摘要
研究了Mbius变换f,g不动点的关系对它们的极限球或超球之间位置的影响。证明了,在〈g,f〉离散群且二者的不动点集合相等时,当g,f为抛物变换时,范数越大,极限球越小;当g,f为双曲变换时,迹越大,超球越小;当g,f为椭圆变换时,旋转角越大,超球越小。如果〈g,f〉是离散群且二者没有公共不动点,并且f,g共轭时,则存在一个正数,使得f,g的极限球或超球不相交。
This article is concerned with the relationship between fixed points and hypercyclics or horo-balls of Mobius transformations in discrete groups.The main research achievements are as follows： If〈g,f〉is discrete andg,fhave the same fixed points,then the one which has a larger norm has a smaller hypercyclic wheng,fare parabolic.The one which has a larger trace has a smaller horoball wheng,fare hyperbolic.The one which has a larger rotation angle has a smaller horoball wheng,fare elliptic.If〈g,f〉is discrete andg,fhave no fixed point,andfis conjugate tog,then there exists a positive number such that the hypercyclics or horoballs ofg,fhave no intersection.
出处
《中国海洋大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第4期122-126,共5页
Periodical of Ocean University of China
基金
留学归国人员启动基金项目(1501-091944)资助
关键词
Mbius变换
不动点
极限球
超球
Mobius transformations
fixed points
hypercyclics
horoballs
