Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5
By Jibin Li, H. Chan, K. Chung. Science China Mathematics, 2002
52 citations recorded by the source corpus.
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 + I)2 - 1 for the perturbed Hamiltonian systems.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d15ffbb6bbbc66a110bcbe1d4d8ab82cef15f527
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields (2005, methodology): “, see [1,6,7]), the best results published so far are: [8] showed H(2) 4, [9,10] gave H(3) 12, and [11] obtained H(5) 23 for a Z6-equivariant Hamiltonian system using the method of detection functions.”