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

Bassem Ben Hamed; Ameni Gargouri; Lubomir Gavrilov

doi:10.1016/j.jmaa.2014.11.018

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

Bassem Ben Hamed
, Ameni Gargouri
, Lubomir Gavrilov

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	774-784
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	424
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.11.018
State	Published - 1 Apr 2015
Externally published	Yes

Keywords

16th Hilbert problem
Limit cycles
Zeros of elliptic integrals depending on parameters

Access to Document

10.1016/j.jmaa.2014.11.018

Cite this

@article{11f50ddd65e04d0fbe47faa9cae958a0,

title = "Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain",

abstract = "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.",

keywords = "16th Hilbert problem, Limit cycles, Zeros of elliptic integrals depending on parameters",

author = "\{Ben Hamed\}, Bassem and Ameni Gargouri and Lubomir Gavrilov",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = apr,

day = "1",

doi = "10.1016/j.jmaa.2014.11.018",

language = "English",

volume = "424",

pages = "774--784",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

AU - Ben Hamed, Bassem

AU - Gargouri, Ameni

AU - Gavrilov, Lubomir

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

AB - 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.

KW - 16th Hilbert problem

KW - Limit cycles

KW - Zeros of elliptic integrals depending on parameters

UR - https://www.scopus.com/pages/publications/84920562641

U2 - 10.1016/j.jmaa.2014.11.018

DO - 10.1016/j.jmaa.2014.11.018

M3 - Article

AN - SCOPUS:84920562641

SN - 0022-247X

VL - 424

SP - 774

EP - 784

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this