Multiplicity of Invariant Algebraic Curves and Darboux Integrability

2000/09/02 by Jaume Llibre, Llibre, Jaume, Jorge Vitório Pereira +2
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.DS

paper · pdf · doi:10.48550/arxiv.math/0009020

16 pages, LaTeX

arxiv created 2000/09/02 · openalex publication_date 2000/09/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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