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