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

Bassem Ben Hamed; Ameni Gargouri; Lubomir Gavrilov

doi:10.1016/j.bulsci.2019.102796

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

Journal article

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

Bassem Ben Hamed, Ameni Gargouri and Lubomir Gavrilov

Bulletin des sciences mathématiques, Vol.157, p.102796

12/2019

DOI: https://doi.org/10.1016/j.bulsci.2019.102796

Abstract

Duffing oscillator

Limit cycles

Zeros of elliptic integrals

We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we compute the general form of M2 and study its zeros in a suitable complex domain.

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Title: Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
Creators - without role: Bassem Ben Hamed - Ecole Nationale d'Electronique et des Télécommunications de Sfax, Route de Tunis km 10, BP 1163, 3021 Sfax, Tunisie
Ameni Gargouri - Laboratoire de Mathématiques d'Orsay
Lubomir Gavrilov - Toulouse Mathematics Institute
Publication Details: Bulletin des sciences mathématiques, Vol.157, p.102796
Publisher: Elsevier Masson SAS
Identifiers: 9925991808331
Academic Unit: Prince Sattam Bin Abdulaziz University
Language: English
Resource Type: Journal article