Vector Fields, Invariant Varieties and Linear Systems
Dynamical Systems
2010-04-05 v1 Algebraic Geometry
Abstract
We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criteria for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields and a generalization of Darboux's criteria. We also provide a new proof of Gomez-Mont's result on foliations with all leaves algebraic.
Keywords
Cite
@article{arxiv.math/0011205,
title = {Vector Fields, Invariant Varieties and Linear Systems},
author = {Jorge Vitorio Pereira},
journal= {arXiv preprint arXiv:math/0011205},
year = {2010}
}
Comments
15 pages, Latex