On the Limit Cycles Bifurcating from the Periodic Orbits of a Hamiltonian System

Abstract

Altres ajuts: Reial Acadèmia de Ciències i Arts de BarcelonaThis paper concerns the weak 16th Hilbert problem and considers the Hamiltonian center a: = -y2n-1, a: = x2n-1, and we perturb it by all polynomials of degree 2n-1 for n = 2, 3, 4, 5, 6, 7, 8. We prove that the maximum number of limit cycles that can bifurcate from the periodic orbits of this center for n = 2, 3, 4, 5, 6, 7, 8, under the mentioned perturbations and using the averaging theory of first order, is 1, 4, 3, 2, 5, 6, 7, respectively