TY - JOUR
T1 - Some lower bounds for h(n) in Hilbert's 16th problem
AU - Li, Jibin
AU - Chan, H. S Y
AU - Chung, K. W.
PY - 2002
Y1 - 2002
N2 - For some perturbed Z2-(or Z4-)equivariant planar Hamiltonian vector field sequnces of degree n (n = 2k - 1 and n = 3 × 2k-1 - 1, k = 2, 3,...), some new lower bounds for H(n) in Hilbert's 16th problem and configurations of compound eyes of limit cycles are given, by using the bifurcation theory of planar dynamical systems and the quadruple transformation method given by Christopher and Lloyd. It gives rise to more exact results than Ref.[6].
AB - For some perturbed Z2-(or Z4-)equivariant planar Hamiltonian vector field sequnces of degree n (n = 2k - 1 and n = 3 × 2k-1 - 1, k = 2, 3,...), some new lower bounds for H(n) in Hilbert's 16th problem and configurations of compound eyes of limit cycles are given, by using the bifurcation theory of planar dynamical systems and the quadruple transformation method given by Christopher and Lloyd. It gives rise to more exact results than Ref.[6].
KW - Distributions of limit cycles
KW - Hilbert's 16th problem
KW - Perturbed planar hamiltonian systems
KW - Second bifurcation
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U2 - 10.1007/BF02969411
DO - 10.1007/BF02969411
M3 - RGC 21 - Publication in refereed journal
VL - 3
SP - 345
EP - 360
JO - Qualitative Theory of Dynamical Systems
JF - Qualitative Theory of Dynamical Systems
SN - 1575-5460
IS - 2
ER -