三阶齐次微分方程的几何
The geometry of Chazy's homogeneous third-order differential equations
摘要：
查齐研究了一个家庭的齐次三阶自治微分方程。它们是在某个类内只承认单值解的那些。这些方程中的每一个都产生复三维空间中的多项式向量场。对于几乎所有的这些向量场，一个一般轨道的Zebriki闭包产生一个仿射曲面，该曲面具有一个全纯向量场，该向量场具有唯一的单值解。我们对这些表面进行分类，并将这种分类与Rebelo和作者最近的结果相关联。
英文摘要：
Chazy studied a family of homogeneous third-order autonomous differential equations. They are those, within a certain class, admitting exclusively single-valued solutions. Each one of these equations yields a polynomial vector field in complex three-dimensional space. For almost all of these these vector fields, the Zariski closure of a generic orbit yields an affine surface endowed with a holomorphic vector field that has exclusively single-valued solutions. We classify these surfaces and relate this classification to recent results of Rebelo and the author.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
