MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION

doi:10.3934/dcds.2017135

CSpace > 数学所

	MINIMALITY OF p-ADIC RATIONAL MAPS WITH GOOD REDUCTION
	Fan, Aihua 1,2; Fan, Shilei 1,3; Liao, Lingmin 4; Wang, Yuefei5
	2017-06-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN	1078-0947
卷号	37 期号:6 页码:3161-3182
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)).
关键词	p-adic dynamical system minimal decomposition projective line good reduction rational map
DOI	10.3934/dcds.2017135
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000395905000011
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	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.