TY - JOUR
T1 - Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5
AU - Li, Jibin
AU - Chan, H. S. Y.
AU - Chung, K. W.
PY - 2002/7
Y1 - 2002/7
N2 - A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ≥ (2k + 1)2 - 1 for the perturbed Hamiltonian systems.
AB - A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ≥ (2k + 1)2 - 1 for the perturbed Hamiltonian systems.
KW - Equivariant vector field
KW - Hilbert's 16th problem
KW - Limit cycle
KW - Method of detection function
KW - Polynomial system
UR - http://www.scopus.com/inward/record.url?scp=52649094247&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-52649094247&origin=recordpage
M3 - 22_Publication in policy or professional journal
VL - 45
SP - 817
EP - 826
JO - Science in China, Series A: Mathematics
JF - Science in China, Series A: Mathematics
SN - 1006-9283
IS - 7
ER -