A class of polynomial planar vector fields with polynomial first integral
Classical Analysis and ODEs
2014-10-15 v1 Algebraic Geometry
Abstract
We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral. In addition, we solve the Poincar\'e problem for the class of systems which admit a polynomial first integral as above in the sense that the degree of the minimal first integral can be computed from the reduction of singularities of the corresponding vector field.
Cite
@article{arxiv.1410.3652,
title = {A class of polynomial planar vector fields with polynomial first integral},
author = {A. Ferragut and C. Galindo and F. Monserrat},
journal= {arXiv preprint arXiv:1410.3652},
year = {2014}
}