Resumen de Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields

Rasoul Asheghi, Arefeh Nabavi

• In this paper, we study the number of limit cycles in the perturbed Hamiltonian system dH=εF1+ε2F2+ε3F3 with Fi, the vector valued homogeneous polynomials of degree i and 4-i for i=1,2,3, and small positive parameter ε. The Hamiltonian function has the form H=y2/2+U(x), where U is a univariate polynomial of degree four without symmetry. We compute higher order Melnikov functions until we obtain reversible perturbations. Then we find the upper bounds for the number of limit cycles that can bifurcate from the periodic orbits of dH=0.