This paper is concerned with a quadratic reversible and non-Hamiltonian system with one center of genus one. By using the properties of related elliptic integrals and the geometry of some planar curves defined by them, we prove that the cyclicity of the period annulus of the considered system under small quadratic perturbations is two. This verifies Gautier's conjecture about the cyclicity of the related period annulus.
PENG, LINPING and SUN, YANNAN
"The cyclicity of the period annulus of a quadratic reversible system with one center of genus one,"
Turkish Journal of Mathematics: Vol. 35:
4, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss4/7