Abstract: In the study of the perturbation of Hamiltonian systems, the first order Melnikov functions plays an important role. By finding its zeros we can find limit cycles. By analyzing its analytical property we can find its zeros. In the talk we present some methods to find its zeros through the expansions of the Melnikov function at a Hamiltonian value corresponding to an elementary center, nilpotent center or a homoclinic or heteroclinic loop with hyperbolic saddles or nilpotent critical points. Then we list some results on the limit cycle bifurcation by using the first coeffcients of the expansions.
Seminarsko predavanje bo v četrtek 18. avgusta 2011 ob 15:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje. Vljudno vabljeni vsi zainteresirani, tudi študenti.