The Poincare center-focus problem for a class of higher order polynomial differential systems
Classical Analysis and ODEs
2019-05-01 v1
Abstract
In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these differential systems to have a center at origin point by using a different method from the previous references. By this I can obtain all the focal values of these systems for an arbitrary n and their expressions are succinct and beautiful. I believe that the idea and method of this article can be used to solve the center-focus problem of more high-order polynomial differential systems.
Keywords
Cite
@article{arxiv.1811.11893,
title = {The Poincare center-focus problem for a class of higher order polynomial differential systems},
author = {Zhengxin Zhou},
journal= {arXiv preprint arXiv:1811.11893},
year = {2019}
}