具有Painlevé性质的一阶方程
Order one equations with the Painlevé property
摘要：
具有Painlevé性质的微分方程由于其在数学的许多分支中的出现以及在物理学中的应用而得到了广泛的研究。虽然一个现代的，微分代数治疗一阶方程出现之前，与经典理论的联系没有。使用技术从代数几何，我们提供了古典和现代的治疗之间的联系，并与微分伽罗瓦论的帮助下，一个新的分类是派生的，无论是对特征0和p。
英文摘要：
Differential equations with the Painlevé property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order one equations appeared before, the connection with the classical theory did not. Using techniques from algebraic geometry we provide the link between the classical and the modern treatment, and with the help of differential Galois theory a new classification is derived, both for characteristic 0 and p.
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。
