Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian

Fatma Sassi; Ameni Gargouri; Lubomir Gavrilov; Bassem Ben Hamed

doi:10.1007/s00013-020-01495-8

Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian

Fatma Sassi
, Ameni Gargouri
, Lubomir Gavrilov
, Bassem Ben Hamed

Mathematics

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

Abstract

We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system x^′= y, y^′= x- x³, has two irreducible components of co-dimension two in the parameter space. One of them corresponds to the Hamiltonian stratum, the other to systems which are a polynomial pull back of an appropriate linear system.

Original language	English
Pages (from-to)	567-574
Number of pages	8
Journal	Archiv der Mathematik
Volume	115
Issue number	5
DOIs	https://doi.org/10.1007/s00013-020-01495-8
State	Published - 1 Nov 2020

Keywords

Center-focus problem
Cubic vector field
Limit cycles

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10.1007/s00013-020-01495-8

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title = "Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian",

abstract = "We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system x′= y, y′= x- x3, has two irreducible components of co-dimension two in the parameter space. One of them corresponds to the Hamiltonian stratum, the other to systems which are a polynomial pull back of an appropriate linear system.",

keywords = "Center-focus problem, Cubic vector field, Limit cycles",

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

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AU - Sassi, Fatma

AU - Gargouri, Ameni

AU - Gavrilov, Lubomir

AU - Hamed, Bassem Ben

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system x′= y, y′= x- x3, has two irreducible components of co-dimension two in the parameter space. One of them corresponds to the Hamiltonian stratum, the other to systems which are a polynomial pull back of an appropriate linear system.

AB - We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system x′= y, y′= x- x3, has two irreducible components of co-dimension two in the parameter space. One of them corresponds to the Hamiltonian stratum, the other to systems which are a polynomial pull back of an appropriate linear system.

KW - Center-focus problem

KW - Cubic vector field

KW - Limit cycles

UR - https://www.scopus.com/pages/publications/85087286988

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DO - 10.1007/s00013-020-01495-8

M3 - Article

AN - SCOPUS:85087286988

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SP - 567

EP - 574

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 5

ER -

Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian

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Keywords

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