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arXiv · 2409.01751

New solutions of the Poincar\'e Center Problem in degree 3

Hans-Christian von Bothmer
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Abstract

Let $\omega$ be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi-homogeneous we we present new criteria that guarantee Darboux integrability. We use this to construct previously unknown components of the center variety in degree 3.

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Hans-Christian von Bothmer. 2024-09-03. New solutions of the Poincar\'e Center Problem in degree 3. https://arxiv.org/abs/2409.01751

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