具有非解析中心条件的无特征方向系统

Pub Date : 2023-12-01 DOI:10.1134/s0012266123120030

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引用次数: 0

摘要

摘要获得了一个具有退化奇点且无特征方向的五阶实自微分系统。在系统奇点为单色性的系统参数集边界点上的非解析函数决定了在给定点上中心的必要和充分条件。在违反其解析性的点上计算该函数的渐近表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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System without Characteristic Directions with a Nonanalytic Center Condition

Abstract

A real autonomous differential system of the fifth degree with a degenerate singular point without characteristic directions is obtained. The necessary and sufficient condition for the center at a given point is determined by a function that is not analytic at the boundary point of the set of system parameters for which the singular point of the system is monodromic. An asymptotic representation of this function is calculated at the point where its analyticity is violated.

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