Bifurcation Of Limit Cycles For A Planar Near-integrable System With Multiple Parameters

In this thesis,we consider limit cycle bifurcations of a planar near-integrable system with multiple parameters.The unperturbed system has a center and two invariant straight lines.By using the first order Melnikov function method for near Hamiltonian systems with multiple parameters,we obtain a lower bound of the maximal number of limit cycles bifurcated from the period annulus under nth degree perturbations.Moreover,we find that 2[(n+1)/2]limit cycles can appear by perturbing a quadratic center under n-th degree perturbations for n?3,which improves some known results on this aspect.