实多项式向量场在$\sss^n$上的达布可积性理论
Darboux theory of integrability for real polynomial vector fields on $\sss^n$
摘要：
本文是关于多项式向量场的达布可积性理论的综述，首先是在$\R^n$中，其次是在$n$维球面$\sss^n$中.我们还提供了新的结果的最大数量的平行线和子午线的多项式向量场$\X$ $\sss^n$可以在其程度的函数。这些结果在某种意义上扩展了关于$\R^n$中多项式向量场$\Y$可以具有的超平面的最大数目的已知结果，该超平面是$\Y$的次数的函数。
英文摘要：
This is a survey on the Darboux theory of integrability for polynomial vector fields, first in $\R^n$ and second in the $n$-dimensional sphere $\sss^n$. We also provide new results about the maximum number of parallels and meridians that a polynomial vector field $\X$ on $\sss^n$ can have in function of its degree. These results in some sense extend the known result on the maximum number of hyperplanes that a polynomial vector field $\Y$ in $\R^n$ can have in function of the degree of $\Y$.
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