QQ客服 官方微博 反馈留言

	CODIMENSION ONE STRUCTURALLY STABLE CHAIN CLASSES
	Wen, Xiao ; Wen, Lan
	2016
关键词	Structural stability chain component homoclinic class hyperbolicity HOMOCLINIC CLASSES HYPERBOLICITY DIFFEOMORPHISMS LEMMA COMPONENTS
英文摘要	The well-known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable, then the chain recurrent set is hyperbolic. It is natural to ask if this type of result is true for an individual chain class, that is, whether or not every structurally stable chain class is hyperbolic. Regarding the notion of structural stability, there is a subtle difference between the case of a whole system and the case of an individual chain class. The latter is more delicate and contains additional difficulties. In this paper we prove a result of this type for the latter, with an additional assumption of codimension 1. Precisely, let f be a diffeomorphism of a closed manifold M and let p be a hyperbolic periodic point of f of index 1 or dim M - 1. We prove if the chain class of p is structurally stable, then it is hyperbolic. Since the chain class of p is not assumed in advance to be locally maximal, and since the counterpart of it for the perturbation g is defined not canonically but indirectly through the continuation p(g) of p, the proof is quite delicate.; NSFC [11301018, 11231001]; Balzan Research Project of J. Palis; SCI(E); ARTICLE; wenxiao@buaa.edu.cn; lwen@math.pku.edu.cn; 6; 3849-3870; 368
语种	英语
出处	SCI
出版者	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/438135]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wen, Xiao,Wen, Lan. CODIMENSION ONE STRUCTURALLY STABLE CHAIN CLASSES. 2016-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。