Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in a Complex domain

Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov

Published 2016-03-24Version 1

We consider arbitrary one-parameter cubic deformations of the Duffing oscillator $x"=x-x^3$. In the case when the first Melnikov function $M_1$ vanishes, but $M_2\neq 0$ we compute the general form of $M_2$ and study its zeros in a suitable complex domain.