TY - JOUR
T1 - The cyclicity of the period annulus of a quadratic reversible system with one center of genus one
AU - Peng, Linping
AU - Sun, Yannan
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - A quadratic reversible system with one center of genus one
KW - Bifurcation of limit cycles
KW - Cyclicity
KW - Period annulus
KW - Quadratic perturbations
UR - https://www.scopus.com/pages/publications/81555200742
U2 - 10.3906/mat-1007-363
DO - 10.3906/mat-1007-363
M3 - 文章
AN - SCOPUS:81555200742
SN - 1300-0098
VL - 35
SP - 667
EP - 685
JO - Turkish Journal of Mathematics
JF - Turkish Journal of Mathematics
IS - 4
ER -