极限集的性态

The Behaviour of Limit Sets

本文首先给出了n维微分流形M^n上C^1阶1维叶层极根集有关连通性,弧连通性的几个结果,其次定义了1维、2维,…,k维例外叶(例外轨道)的概念。给出了R^3上含有1维例外叶、2维例外叶的叶层的洌子,包括了D'Heedene关于Poincarè-Bendixson定理的反例。

First, in this paper, we give some results about the connectedness and arcwise connectedness of the limit sets of one-dimension C’ (r>1) foliations on n-dimension C’ differentiable manifolds M. Then, we define 1-dimension. 2-dimension, …, k-dimension exceptional leaves and give the examples of foliations contaiuing 1-dimension, 2-dimension exceptional leaves on R^3induding the D’Heedene’s counterexample about Poincare-Bendixsion theorem.