Quadratic perturbations of a quadratic reversible center of genus one

Abstract

In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al.

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

“…• quadratic systems with a center [35,83,92,117,118,119,128,141,175,176,177,178,179,191,193,208,214,234],…”