Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

https://doi.org/10.1016/j.bulsci.2019.102796Get rights and content
Under an Elsevier user license
open archive

Abstract

We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x=xx3. In the case when the first Melnikov function M1 vanishes, but M20 we compute the general form of M2 and study its zeros in a suitable complex domain.

Keywords

Limit cycles
Zeros of elliptic integrals
Duffing oscillator

Cited by (0)