arXiv:math/0009020 Abstract

arXiv:math/0009020 [math.DS]Abstract References Reviews Resources

Multiplicity of Invariant Algebraic Curves and Darboux Integrability

Published 2000-09-02Version 1

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.

Comments: 16 pages, LaTeX

Categories: math.DS

Keywords: invariant algebraic curve, darboux integrability, multiplicity, polynomial vector field, closer look

Related articles: Most relevant | Search more

arXiv:math/0505019 [math.DS] (Published 2005-05-02, updated 2005-09-30)

Entropy via multiplicity

Boris Kruglikov, Martin Rypdal

arXiv:0904.4189 [math.DS] (Published 2009-04-27, updated 2009-04-30)

Quadratic vector fields with invariant algebraic curve of large degree

R. Ramirez, N. Sadovskaia

arXiv:math/9909091 [math.DS] (Published 1999-09-16)

Isochronicity and Commutation of Polynomial Vector Fields