On the cyclicity of the period annulus of quadratic Hamiltonian triangle vector field
This paper is concerned with the cyclicity of the period annulus of quadratic Hamiltonian triangle vector field under quadratic perturbations. This problem has been studied by Iliev (J. Differential Equations {\bf 128}(1996)), based on the displacement function obtained by Żoładek (J. Differential Equations {\bf 109}(1994)). Recently, P. Mardešić etc. (J. Dynamical and Control Systems {\bf 17}(2011)) studied unfoldings of the Hamiltonian triangle within quadratic vector fields. It turned out that the displacement function is not precise of the form given by Żoładek. Using the corrected form of the displacement function obtained by P. Mardešić etc, it is proved in this paper that the cyclicity of the period annulus under quadratic perturbations is equal to three.