论文部分内容阅读
同宿环的稳定性在研究同宿分支时起很重要的作用.对于平面系统,这一问题已有不少结果(见冯贝叶,中国科学,A辑,1991,(7):673—684);嗣后《科学通报》(1992,37(21):1935—1937)发表了孙建华的“三维弱同宿吸引子的判别准则”,其中研究三维系统x=F(X),X∈R~3,F∈C~2.假设此系统有同宿环L.孙建华首先定义了“弱吸引子”的概念:定义1 弱吸引子(弱排斥子)是一个不可分解的闭不变集L,满足如下性质:给定ε>0,在L的ε-邻域中存在Lebesgue测度为正的集合U,使得只要X∈U,则X的ω(α)极限集就包含在L中,且X的前向(后向)轨道O~+(X)(O~-(X))就包含在U中.
The stability of homoclinic rings plays a very important role in the study of the homoclinic branch, which has had many consequences for planar systems (see Feng Beiye, Chinese Science, Series A, 1991, (7): 673-684) ; And later Science Bulletin (1992,37 (21): 1935-1937) published Sun Jianhua’s criterion for the determination of three-dimensional weak homoclinic attractors, in which three-dimensional systems x = F (X), X∈R ~ F∈C ~ 2. Assume that this system has the homoclinic ring L. Sun Jianhua first defines the concept of “weak attractor”: Definition 1 The weak attractor (weak exclusion) is an indecomposable closed invariant set L, which satisfies the following properties : Given ε> 0, there exists a set U with positive Lebesgue measure in the ε-neighborhood of L such that the limit set of ω (α) of X is contained in L as long as X∈U, and the forward direction of X (Backward) orbit O ~ + (X) (O ~ - (X)) is included in U.