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Center conditions for nilpotent cubic systems using the Cherkas method

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  • Giné, Jaume

Abstract

In this study, we consider the center problem of a cubic polynomial differential system with a nilpotent linear part. The analysis is based on the application of the Cherkas method to the Takens normal form. The analysis requires many computations, which are verified by employing one algebraic manipulator and extensive use of the computer algebra system called Singular.

Suggested Citation

  • Giné, Jaume, 2016. "Center conditions for nilpotent cubic systems using the Cherkas method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 129(C), pages 1-9.
    • Handle: RePEc:eee:matcom:v:129:y:2016:i:c:p:1-9
    DOI: 10.1016/j.matcom.2016.04.002
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    References listed on IDEAS

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    1. Wu, Yusen & Li, Peiluan & Chen, Haibo, 2015. "Calculation of singular point quantities at infinity for a type of polynomial differential systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 153-173.
    2. Feng, Li & Yirong, Liu & Hongwei, Li, 2011. "Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(12), pages 2595-2607.
    3. Chavarriga, J. & Giné, J. & Sorolla, J., 2002. "Analytic integrability of a class of nilpotent cubic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 489-495.
    4. Llibre, Jaume & Pantazi, Chara, 2016. "Limit cycles bifurcating from a degenerate center," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 1-11.
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