The shape of limit cycles that bifurcate from non-Hamiltonian centers

A method for computing analytically, up to any order of the bifurcation parameter, the shape of the limit cycles from a Hamiltonian center is introduced. This method is the unique explicit procedure in the literature about limit cycles which allows to determine the shape of these bifurcated cycles. The global shape of the bifurcated cycles from a non-Hamiltonian center was computed, when it is perturb by an arbitrary analytic planar vector field. This generalization is not straightforward and presents several technical difficulties.