Multiplicity of Invariant Algebraic Curves and Darboux Integrability
Jaume Llibre, Jorge Vitorio Pereira
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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