Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5 |
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| Authors: | Li Jibin H S Y Chan and K W Chung |
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| Institution: | (1) School of Science, Kunming University of Science and Technology, 650093 Kunming, China;(2) Department of Mathematics, City University of Hong Kong, Hong Kong, China |
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| Abstract: | 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. |
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| Keywords: | Hilbert’ s 16th problem limit cycle equivariant vector field method of detection function polynomial system |
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