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 \.{ Z}o{ \l}adek (J. Differential Equations { \bf 109}(1994)). Recently, P. Marde\v{ s}i\'{ c} 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 \.{ Z}o{ \l}adek. Using the corrected form of the displacement function obtained by P. Marde\v{ s}i\'{ c} etc, it is proved in this paper that the cyclicity of the period annulus under quadratic perturbations is equal to three.
Categories: math.CA