English

Multiplicity of Invariant Algebraic Curves and Darboux Integrability

Dynamical Systems 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0009020,
  title  = {Multiplicity of Invariant Algebraic Curves and Darboux Integrability},
  author = {Jaume Llibre and Jorge Vitorio Pereira},
  journal= {arXiv preprint arXiv:math/0009020},
  year   = {2007}
}

Comments

16 pages, LaTeX