The cyclicity of the period annulus of a quadratic reversible system with one center of genus one

Linping PENG; Yannan SUN

Article Details

The cyclicity of the period annulus of a quadratic reversible system with one center of genus one

Authors:

Linping PENG | Yannan SUN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.667-685

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747900

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

This paper is concerned with a quadratic reversible and  non-Hamiltonian system with one center of genus one.  By using the  properties of related elliptic integrals and the geometry of some  planar curves defined by them, we prove that the cyclicity of the  period annulus of the considered system under small quadratic  perturbations is two.  This verifies Gautier's conjecture about the  cyclicity of the related period annulus.

 

This paper is concerned with a quadratic reversible and  non-Hamiltonian system with one center of genus one.  By using the  properties of related elliptic integrals and the geometry of some  planar curves defined by them, we prove that the cyclicity of the  period annulus of the considered system under small quadratic  perturbations is two.  This verifies Gautier's conjecture about the  cyclicity of the related period annulus.

Article Details

The cyclicity of the period annulus of a quadratic reversible system with one center of genus one

Authors:

Linping PENG | Yannan SUN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.667-685

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747900

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Cyclicity

bifurcation of limit cycles

quadratic perturbations

period annulus

a quadratic reversible system with one center of genus one

Issues

Article Details

The cyclicity of the period annulus of a quadratic reversible system with one center of genus one

Authors: Linping PENG | Yannan SUN

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.667-685

Document Type: Article

Publication Date: 3/2011

Document Language: Turkish

Document ID (Org No.): 2000747900

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Cyclicity

bifurcation of limit cycles

quadratic perturbations

period annulus

a quadratic reversible system with one center of genus one

Issues

Authors:

Linping PENG | Yannan SUN

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.667-685

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747900

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098