3度波恩卡莱中心问题的新解

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-03 DOI:arxiv-2409.01751

Hans-Christian von Bothmer

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引用次数: 0

摘要

让 $\omega$ 是一个平面自治系统，C 是其代数积分曲线的配置。如果 C 的奇点是准均质的，我们就给出了达尔布积分因子或达尔布第一积分存在的新条件。这将用于构造 3 度中心变的新分量。

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New solutions of the Poincaré Center Problem in degree 3

Let $\omega$ be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi homogeneous we give new conditions for existence of a Darboux integrating factor or a Darboux first integral. This is used to construct new components of the center variety in degree 3.

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arXiv - MATH - Dynamical Systems

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