Bifurcation of Limit Cycles by Perturbing Piecewise Hamiltonian Systems

In this paper, the general perturbation of piecewise Hamiltonian systems on the plane is considered. When the unperturbed system has a family of periodic orbits, similar to the perturbations of smooth system, an expression of the first order Melnikov function is derived, which can be used to study the number of limit cycles bifurcated from the periodic orbits. As applications, the number of bifurcated limit cycles of several concrete piecewise systems are presented.