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Analytic integrability of certain resonant saddle

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  • Christopher, Colin
  • Giné, Jaume

Abstract

We provide sufficient conditions of analytic integrability for a family of planar differential system with a p:−q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjectured that the conditions are in fact complete for all families.

Suggested Citation

  • Christopher, Colin & Giné, Jaume, 2021. "Analytic integrability of certain resonant saddle," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921001739
    DOI: 10.1016/j.chaos.2021.110821
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Li, Feng & Li, Hongwei & Liu, Yuanyuan, 2020. "Integrability of resonant saddles in a complex differential system," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

    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).

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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. 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.
    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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