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Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
Journal article   Peer reviewed

Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

Bassem Ben Hamed, Ameni Gargouri and Lubomir Gavrilov
Journal of mathematical analysis and applications, Vol.424(1), pp.774-784
01/04/2015
DOI: https://doi.org/10.1016/j.jmaa.2014.11.018

Abstract

16th Hilbert problem Limit cycles Zeros of elliptic integrals depending on parameters
The cyclicity of the exterior period annulus of the asymmetrically perturbed Duffing oscillator is a well known problem extensively studied in the literature. In the present paper we provide a complete bifurcation diagram for the number of the zeros of the associated Melnikov function in a suitable complex domain.

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