C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS

doi:10.3934/dcds.2018074

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS
	Xiao, Qianying 3; Zheng, Zuohuan1,2
刊名	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
	2018-04-01
卷号	38 期号:4 页码:1809-1832
关键词	Nonsingular flow Morse-Smale system away from horseshoe linear Poincare flow central model
ISSN号	1078-0947
DOI	10.3934/dcds.2018074
英文摘要	This paper focuses on generic properties of continuous dynamical systems. We prove C-1 weak Palis conjecture for nonsingular flows: Morse-Smale vector fields and vector fields admitting horseshoes are open and dense among C-1 nonsingular vector fields. Our arguments contain three main ingredients: linear Poincare flow, Liao's selecting lemma and the adapting of Crovisier's central model. Firstly, by studying the linear Poincare flow, we prove for a C-1 generic vector field away from horseshoes, any non-trivial nonsingular chain recurrent class contains a minimal set which is partially hyperbolic with 1-dimensional center with respect to the linear Poincare flow. Secondly, to understand the neutral behaviour of the 1-dimensional center, we adapt Crovisier's central model. The difficulties are that we can not build invariant plaque family of any time, the periodic point of a flow is not periodic for the discrete time map. Through delicate analysis of the center manifold of a periodic orbit near the partially hyperbolic set, we manage to yield nice periodic points such that their stable manifolds and unstable manifolds are well-placed for transverse intersection.
资助项目	NSF of China[11671382] ; NSF of China[11301512] ; CAS Key Project of Frontier Sciences[QYZDJ-SSW-JSC003] ; Key Lab of Random Complex Structures and Data Sciences CAS ; National Center for Mathematics and Interdisplinary Sciences CAS
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000438812700008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/33414]
专题	应用数学研究所
通讯作者	Xiao, Qianying
作者单位	1.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Xiao, Qianying,Zheng, Zuohuan. C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2018,38(4):1809-1832.
APA	Xiao, Qianying,&Zheng, Zuohuan.(2018).C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,38(4),1809-1832.
MLA	Xiao, Qianying,et al."C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 38.4(2018):1809-1832.