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Multiplicity of Invariant Algebraic Curves and Darboux Integrability

Jaume Llibre·Jorge Vitorio Pereira
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Abstract

We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve the Darboux theory of integrability using these new notions of multiplicity.

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Jaume Llibre, Jorge Vitorio Pereira. 2000-09-02. Multiplicity of Invariant Algebraic Curves and Darboux Integrability. https://arxiv.org/abs/math/0009020

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