阻碍集的计算与分歧问题(英文)

Computation of Obstruction Sets and Bifurcation Problems

由廖山涛提出的阻碍集在其微分动力系统研究中起重要作用．本文先介绍阻碍集的概念及与稳定性问题的关系．然后特别就２维和３维的常微分方程建立其阻碍集的计算公式，并通过一些阻碍集的计算例子予以说明．最后讨论阻碍集与分歧理论之间的密切联系，并探讨进一步研究的方向．

Obstruction sets proposed by Liao Shantao play a crucial role in Liao’s study of differentiable dynamical systems. In this paper we first briefly describe the concept of obstruction sets, and specially pay attention on obstruction sets with the relation to stability problems. Then we establish computing formulas of obstruction sets for ordinary differential equations, in particular for two and three dimensional systems. Some examples of computation of obstruction sets are provided. Finally, we discuss the close relation between obstruction sets and bifurcation problems, and detect further research direction.