Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix

Document Type : Research Paper

Authors

1 School of Mathematics and System Sciences, Beihang University

2 School of Mathematics and System Sciences, Beihang University/The 24th Middle School of Beijing

Abstract

The paper is concerned with the bifurcation of limit cycles in general quadratic
perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix
related to a singularity at infinity in the poincar'{e} disk.
Attention goes to the number of limit cycles produced by the period
annulus under perturbations. By using the appropriate Picard-Fuchs
equations and studying the geometric properties of two planar
curves, we prove that the maximal number of limit cycles bifurcating
from the period annulus under small quadratic perturbations is two.

Keywords

Main Subjects