局部可积向量场的整体可积性定理

Whole Integrability Theorem of Locally Integrable Vector Field

给出了平面向量场的局部可积性条件,通过定义旋转数得到了整体可积性定理,并利用直角形闭路径给出了其证明。

In this paper, locally integrability condition of plane vector field is given at first, then the main theorem of whole integrability theorem is obtained by defining the rotation number, and is proved using the rectangular closed path.