In this thesis, we study Poincar ' e bifurcation for a planar piecewise near-Hamiltonian system with two regions separated by a non-regular separation line, which is formed by two rays starting at the o rigin and such that the angle between them is ??(0, ?) . The unperturbed system is a piecewise linear system having a periodic annulus between the origin and a homoclinic loop aroun d the origin for all ??(0, ?). We give an estimation of the maximal number of the limit cycles which bifurcate from the periodic annulus mentioned above under n-th degree polynomial perturbations.