Multiplicity of invariant algebraic curves and Darboux integrability

Jorge Vitório 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.

Anexos:

• mult.dvi