Perturbations of quadratic centers of genus one
Dynamical Systems
2011-03-30 v2 Classical Analysis and ODEs
Abstract
We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the essential one-parameter quadratic perturbations which produce the maximal number of limit cycles. We compute the associated Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit cycles. To illustrate our approach, we determine the cyclicity of the annuli of two particular reversible systems.
Keywords
Cite
@article{arxiv.0705.1609,
title = {Perturbations of quadratic centers of genus one},
author = {Sebastien Gautier and Lubomir Gavrilov and Iliya D. Iliev},
journal= {arXiv preprint arXiv:0705.1609},
year = {2011}
}
Comments
28 pages