Limit Cycles Bifurcating From Nilpotent Critical Points Of Near-hamiltonian Systems

In this paper, we investigate limit cycles bifurcating near a center or a focus ofNear-Hamiltonian systems. Using the method of power series and qualitative analysis,we obtain the classification of singular point in the Higher-order Hamiltonian system;weestablish an algorithm based on the new proof and code programs using the computeralgebra program)Mathmatica; we consider the bifurcation of limit cycles of symmetricnear-Hamiltonian systems near nilpotent centers.In Chapter1, we introduce some results of the second part of Hilbert’s16thproblem and the corresponding weakened problem,the bifurcation theory and methodsof dynamical systems, and then list our main work.In Chapter2, we study the limit cycles bifurcation of Near-Hamiltonian system.we establish an algorithm based on the new proof and present code programs usingthe computer algebra program)Mathmatica.In Chapter3, Using the method of chapter2, we obtain the classification of nilpo-tent singular point in the quartic Hamiltonian system.In Chapter4, we study the limit cycles bifurcating near (nilpotent or elemen-tary) centers of symmetric near-Hamiltonian systems by the computer algebra program)Mathmatica.