论文标题
Chazy方程的杆奇异点不稳定
Instability of pole singularities for the Chazy equation
论文作者
论文摘要
我们证明，Chazy方程的负共振（在Painlevé分析的三个方案中）可能与IT Sgroup-Variance属性直接相关。这些共振表明在这种情况下，极是极力奇异性的不稳定。根据方程中参数的值，不稳定的孤立极可能会变成熟悉的自然边界，或分为几个孤立的奇异点。在第一种情况下，可以给出涉及指数较小校正的收敛串联表示。这可以调解一些早期的方法来解释负共振。 另一方面，我们还证明了最大阳性谐振数量稳定的极点奇异性是稳定的。证据依赖于非线性紫红色方程的一般特性。
We prove that the negative resonances of the Chazy equation (in thesense of Painlevé analysis) can be related directly to it sgroup-invariance properties. These resonances indicate in this case the instability of pole singularities. Depending on the value of a parameter in the equation, an unstable isolated pole may turn into the familiar natural boundary, or split into several isolated singularities. In the first case, a convergent series representation involving exponentially small corrections can be given. This reconciles several earlier approaches to the interpretation of negative resonances. On the other hand, we also prove that pole singularities with the maximum number of positive resonances are stable. The proofs rely on general properties of nonlinear Fuchsian equations.
