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Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems

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  • Giné, Jaume
  • Llibre, Jaume

Abstract

We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.

Suggested Citation

  • Giné, Jaume & Llibre, Jaume, 2017. "Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 130-131.
    • Handle: RePEc:eee:chsofr:v:96:y:2017:i:c:p:130-131
    DOI: 10.1016/j.chaos.2017.01.014
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    References listed on IDEAS

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    1. Giné, Jaume & Valls, Claudia, 2016. "Integrability conditions of a resonant saddle in Liénard-like complex systems," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 139-141.
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    Cited by:

    1. Christopher, Colin & Giné, Jaume, 2021. "Analytic integrability of certain resonant saddle," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Wu, Yusen & Yan, Jinling & Zhang, Cui & Li, Feng, 2022. "Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Ferčec, Brigita & Giné, Jaume, 2019. "Blow-up method to compute necessary conditions of integrability for planar differential systems," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 16-24.

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    1. Wu, Yusen & Yan, Jinling & Zhang, Cui & Li, Feng, 2022. "Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Christopher, Colin & Giné, Jaume, 2021. "Analytic integrability of certain resonant saddle," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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