Periodic orbits associated to Hamiltonian functions of degree four

Abstract

We consider the Hamiltonian polynomial function H of degree fourth given by either H (x, y, px, py) = (+) + (x2 +y2) + V3(x;y) + V4(x,y), or H (x, y, px, py) = (- + ) + (-x2 +y2) + V3 (x, y) + V4 (x, y), where V3 (x, y) and V4 (x, y) are homogeneous polynomials of degree three and four, respectively. Our main objective is to prove the existence and stability of periodic solutions associated to H using the classical averaging method.