On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91⊃[C11+2(C32⊃2C12)]. These results in the paper are useful for the study of the weakened Hilbert’s 16th problem.