Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones

In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove if central subsystem, i.e. defined between lines, has real center and other subsystems have centers or saddles, then at least appear after perturbations annulus. For this, zeros Melnikov function for present normal form order to simplify computations.