定向曲面向量场的弱伪轨追踪
Weakly tracking of vector fields on oriented surfaces
称一个向量场具有弱伪轨追踪性质,如果对任意(ε>0)存在 (d>0)满足对任意 (d)-伪轨,存在一条真轨道使得该伪轨包含在真轨道的(ε)邻域内。本文证明了,在定向光滑闭曲面上,一个向量场包含于具有弱伪轨追踪性质向量场集合的 (C^1) 内部,当且仅当该向量场是结构稳定的。
It is called that a vector field has the weakly shadowing propertyif for any (ε>0) there is (d>0) such that each (d)-pseudoorbit is contained in the (ε)-neighborhood of an exact orbit.In this paper it shows that on an oriented smoothly closed surface, a vector field is in the (C^1) interior of the set of vectorfields satisfying the weakly shadowing property if and only if it is structurally stable.
刘忠杰、李明
数学
基础数学向量场弱伪轨追踪Kupka-Smale结构稳定
pure mathematicsvector fieldsweakly shadowingKupka-Smalestructure stability.
刘忠杰,李明.定向曲面向量场的弱伪轨追踪[EB/OL].(2016-01-08)[2025-08-03].http://www.paper.edu.cn/releasepaper/content/201601-183.点此复制
评论