Bifurcations Of Limit Cycles For Hamilton Systems

In this thesis,the limit cycles bifurcated from some kinds of polynomial system are investigated using the methods of bifurcation theory and qualitative analysis.There are five parts in this thesis.In the first part,we introduce the background,history and development of the qualitative and bifurcation theory of differential equations,some present results and our main work.The second section is the introduction of the basis and basic theory of the qualitative and bifurcation theory of differential equations.In the third section,we consider the number of zeros of the Abelian integrals for a septic Hamiltonian system with global centre under quintic perturbations,using the Picard-Fuchs equation.In the fourth section,we consider the Abelian integrals for a quintic Hamiltonian system with global centre under 2n +1-order perturbations.And we hold the upper bound of the numbers using the same methods and give the proof of n = 2,3.In the last section,following from section third and fourth,we deduce the kinds of Hamiltonian systems into 2m +1 -order.Discussing the Abelian integrals and holding the numbers of zeros.