C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS

doi:10.3934/dcds.2018074

CSpace > 应用数学研究所

	C-1 WEAK PALIS CONJECTURE FOR NONSINGULAR FLOWS
	Xiao, Qianying 1; Zheng, Zuohuan2,3
	2018-04-01
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN	1078-0947
卷号	38 期号:4 页码:1809-1832
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.
关键词	Nonsingular flow Morse-Smale system away from horseshoe linear Poincare flow central model
DOI	10.3934/dcds.2018074
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000438812700008
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/33414
专题	应用数学研究所
通讯作者	Xiao, Qianying
作者单位	1.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, 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.