Preprint A08/2001
Multiplicity of invariant algebraic curves and Darboux integrability

Jorge VitÃ³rio Pereira | Llibre, Jaume

**Keywords: **
Multiplicity | invariant curves | vector fields

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.