Algebraic Multiplicity and the Poincar\'{e} Problem
Classical Analysis and ODEs
2023-09-29 v1
Abstract
In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the system at the singular points. A method for computing the algebraic multiplicity using Newton polygon is also presented.
Cite
@article{arxiv.2309.16392,
title = {Algebraic Multiplicity and the Poincar\'{e} Problem},
author = {Jinzhi Lei and Lijun Yang},
journal= {arXiv preprint arXiv:2309.16392},
year = {2023}
}
Comments
15pages, 1 figures