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MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION

文献类型：期刊论文

作者Fan, Aihua1,2; Fan, Shilei1,3; Liao, Lingmin4; Wang, Yuefei5
刊名DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
出版日期2017-06-01
卷号37期号:6页码:3161-3182
关键词p-adic dynamical system minimal decomposition projective line good reduction rational map
ISSN号1078-0947
DOI10.3934/dcds.2017135
英文摘要A rational map with good reduction in the field Q(p) of p-adic numbers defines a 1-Lipschitz dynamical system on the projective line IP1 (Q(p)) over Q(p). The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, P1 (Q(p)) is decomposed into three parts: finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime p, a criterion of minimality for rational maps with good reduction is obtained. When p = 2, a condition in terms of the coefficients of the rational map is proved to be necessary for the map being minimal and having good reduction, and sufficient for the map being minimal and 1-Lipschitz. It is also proved that a rational map having good reduction of degrees 2, 3 and 4 can never be minimal on the whole space P-1 (Q(2)).
资助项目NSF of China[11471132] ; NSF of China[11401236] ; NSF of China[11231009] ; self-determined research funds of CCNU[CCNU17QN0009]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000395905000011
出版者AMER INST MATHEMATICAL SCIENCES-AIMS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/222]  
专题数学所
通讯作者Fan, Shilei
作者单位1.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
2.Univ Picardie Jules Verne, CNRS, LAMFA, UMR 7352, 33 Rue St Leu, F-80039 Amiens 1, France
3.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
4.Univ Paris Est Creteil, LAMA, UMR 8050, CNRS, 61 Ave Gen Gaulle, F-94010 Creteil, France
5.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Fan, Aihua,Fan, Shilei,Liao, Lingmin,et al. MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2017,37(6):3161-3182.
APA Fan, Aihua,Fan, Shilei,Liao, Lingmin,&Wang, Yuefei.(2017).MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,37(6),3161-3182.
MLA Fan, Aihua,et al."MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 37.6(2017):3161-3182.

入库方式： OAI收割

来源：数学与系统科学研究院

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