The pointwise convergence of p-adic Mobius maps

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	The pointwise convergence of p-adic Mobius maps
其他题名	The pointwise convergence of p-adic Mobius maps
	Wang YueFei; Yang JingHua
	2014
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	57 期号:1 页码:1-8
摘要	The convergence of linear fractional transformations is an important topic in mathematics. We study the pointwise convergence of p-adic Mobius maps, and classify the possibilities of limits of pointwise convergent sequences of Mobius maps acting on the projective line P-1(C-p), where C-p is the completion of the algebraic closure of Q(p). We show that if the set of pointwise convergence of a sequence of p-adic Mobius maps contains at least three points, the sequence of p-adic Mobius maps either converges to a p-adic Mobius map on the projective line P-1(C-p), or converges to a constant on the set of pointwise convergence with one unique exceptional point. This result generalizes the result of Piranian and Thron (1957) to the non-archimedean settings.
其他摘要	The convergence of linear fractional transformations is an important topic in mathematics. We study the pointwise convergence of p-adic Mobius maps, and classify the possibilities of limits of pointwise convergent sequences of Mobius maps acting on the projective line P~1(C_p), where C_p is the completion of the algebraic closure of Q_p. We show that if the set of pointwise convergence of a sequence of p-adic Mobius maps contains at least three points, the sequence of p-adic Mobius maps either converges to a p-adic Mobius map on the projective line P~1(C_p), or converges to a constant on the set of pointwise convergence with one unique exceptional point. This result generalizes the result of Piranian and Thron (1957) to the non-archimedean settings.
关键词	p-adic Mobius maps pointwise convergence Berkovich space
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:5040976
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/56533
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Wang YueFei,Yang JingHua. The pointwise convergence of p-adic Mobius maps[J]. SCIENCE CHINA-MATHEMATICS,2014,57(1):1-8.
APA	Wang YueFei,&Yang JingHua.(2014).The pointwise convergence of p-adic Mobius maps.SCIENCE CHINA-MATHEMATICS,57(1),1-8.
MLA	Wang YueFei,et al."The pointwise convergence of p-adic Mobius maps".SCIENCE CHINA-MATHEMATICS 57.1(2014):1-8.