讲座内容：

We study the limit cycles that bifurcate from a heteroclinic loop in a cubic non-elliptic Hamiltonian system by Melnikov functions of any order. The heteroclinic loop connects a non-Morse point and a hyperbolic saddle. We establish the asymptotic expansions of the Melnikov functions near this heteroclinic loop in near-Hamiltonian systems and provide the formulas of its first seven coefficients. For the cubic degenerate Hamiltonian system we derive the expressions of all different order Melnikov functions.The asymptotic expansions of all nonzero Melnikov functions are exactly obtained. Using these expansions, we obtain 3, 5, 6 and 1 limit cycles bifurcating from the heteroclinic loop by the first, second, third and forth order Melnikov functions, respectively