Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field

Abstract

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