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Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5

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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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Authors and Affiliations

  1. School of Science, Kunming University of Science and Technology, 650093, Kunming, China

    Jibin Li

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    H. S. Y. Chan & K. W. Chung

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  1. Jibin Li
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  2. H. S. Y. Chan
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  3. K. W. Chung
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Correspondence to Jibin Li.

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Li, J., Chan, H.S.Y. & Chung, K.W. Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5. Sci. China Ser. A-Math. 45, 817–826 (2002). https://doi.org/10.1360/02ys9090

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  • DOI: https://doi.org/10.1360/02ys9090

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