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

Bassem Ben Hamed; Ameni Gargouri; Lubomir Gavrilov

paper

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

arXiv:1603.07520

Abstract

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.

arXiv comment17 pages, 5 figures, Bulletin des Sciences Mathématiques (1919) to appear. arXiv admin note: substantial text overlap with arXiv:1401.5419