Saddam Hosseyn Benmekideche2023-09-132023-09-132023MTM/3364http://10.10.1.6:4000/handle/123456789/3839The thesis is a study of a special type of piecewise differential systems. Which start by introduce an essential mathematical concepts for differential systems, including periodic orbits, averaging theory, first integrals, Hamiltonian systems, and Filippov systems. Second, we investigate the limit cycles that arise from perturbations of the periodic orbits of the linear differential center. Finally, we have focused on a specific type of piecewise differential system in the plane by dividing the plane into four quadrants, each of which contains a linear Hamiltonian system. Our investigation includes determining the maximum number of limit cycles that can occur in these systems.enThesis