Multiplicity of Invariant Algebraic Curves and Darboux Integrability

@inproceedings{Pereira2000MultiplicityOI,
  title={Multiplicity of Invariant Algebraic Curves and Darboux Integrability},
  author={Jorge Vit{\'o}rio Pereira},
  year={2000}
}
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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