Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by straight line [Formula: see text], where these kinds have a nilpotent center at which comes from combination two cusps both systems. By Poincaré compactification classify phase portraits We must mention that it is extremely rare to find works studying center-focus problem in smooth with nonelementary singular points as did here.