关于Poincaré无穷远处极限环的第四、五例
On Poincaré's Fourth and Fifth Examples of Limit Cycles at Infinity
摘要：
在Henri Poincaré的论文“Mémoire sur les courbes definies par une équation différentielle”中的例子问题中发现了错误。“第七章的例子4和5以及第九章的例子1、2和3都没有庞加莱预言的无穷远处的极限环。相反，它们在无穷远无穷远点上都有不动点。为了理解庞加莱所犯的错误，我们详细研究了例子四和例子五。第四和第五个例子的替代方程建议的基础上的假设，从庞加莱方程中省略的条款。
英文摘要：
Errors are found in example problems from Henri Poincaré's paper ``Mémoire sur les courbes définies par une équation différentielle.'' Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poincaré, examples four and five are studied at length. Replacement equations for the fourth and fifth examples are suggested based on the supposition that terms were omitted from Poincaré's equations.
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