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On some open problems in planar differential systems and Hilbert’s 16th problem

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  • Giné, Jaume

Abstract

This review paper contains a brief summary of topics and concepts related with some open problems of planar differential systems. Most of them are related with 16th Hilbert problem which refers to the existence of a uniform upper bound on the number of limit cycles of a polynomial system in function of its degree. These open problems are proposed as open questions throughout the text. Finally, an extensive bibliography, which does not intend to be exhaustive, is also given.

Suggested Citation

  • Giné, Jaume, 2007. "On some open problems in planar differential systems and Hilbert’s 16th problem," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1118-1134.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:5:p:1118-1134
    DOI: 10.1016/j.chaos.2005.10.057
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    1. Chandrasekar, V.K. & Pandey, S.N. & Senthilvelan, M. & Lakshmanan, M., 2005. "Application of extended Prelle–Singer procedure to the generalized modified Emden type equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1399-1406.
    2. Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
    3. Wu, Yuhai & Han, Maoan & Liu, Xuanliang, 2005. "On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 999-1012.
    4. Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
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    Cited by:

    1. Liu, Yuanyuan & He, Dongping & Huang, Wentao, 2023. "Weak centers and local criticality on planar Z2-symmetric cubic differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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