Résumé:
The 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.
