| 离散群中Mbius变换的公共不动点与极限球和超球的关系 |
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| 引用本文： | 李长军,张坦然.离散群中Mbius变换的公共不动点与极限球和超球的关系[J].中国海洋大学学报(自然科学版),2010,40(4). |
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| 作者姓名： | 李长军 张坦然 |
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| 作者单位： | 中国海洋大学数学科学学院,山东,青岛,266100 |
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| 基金项目： | 留学归国人员启动基金项目 |
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| 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。
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| 关 键 词： | M(o)bius变换 不动点 极限球 超球 |
Hypercyclics,Horoballs and Fixed Points of M(o)bius Discrete Groups |
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| LI Chang-Jun,ZHANG Tan-Ran.Hypercyclics,Horoballs and Fixed Points of M(o)bius Discrete Groups[J].Periodical of Ocean University of China,2010,40(4). |
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| Authors: | LI Chang-Jun ZHANG Tan-Ran |
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| Institution: | LI+Chang-Jun,ZHANG+Tan-Ran(School+of+Mathematical+Science,Ocean+University+of+China,Qingdao+266100,China) |
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| Abstract: | This article is concerned with the relationship between fixed points and hypercyclics or horoballs of M(o)bius transformations in discrete groups. The main research achievements are as follows: If 〈g,f〉 is discrete and g,f have the same fixed points,then the one which has a larger norm has a smaller hypercyclic when g,f are parabolic. The one which has a larger trace has a smaller horoball when g,f are hyperbolic. The one which has a larger rotation angle has a smaller horoball when g,f are elliptic. If 〈g,f〉 is discrete and g,f have no fixed point,and f is conjugate to g,then there exists a positive number such that the hypercyclics or horoballs of g,f have no intersection. |
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| Keywords: | M(o)bius transformations fixed points hypercyclics horoballs |
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