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Blow-up method to compute necessary conditions of integrability for planar differential systems

Author

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  • Ferčec, Brigita
  • Giné, Jaume

Abstract

We provide a method to compute the necessary conditions of integrability for planar differential systems with a weak saddle at the origin. The method is used to characterize the local analytic integrability for resonant saddles of complex systems of the form x˙=px, and y˙=−y+f(y)x,0≠p∈N, with f analytic at the origin and with f(0)=0.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:16-24
    DOI: 10.1016/j.amc.2019.04.007
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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. Antonio Algaba & Cristóbal García & Jaume Giné, 2013. "On the Formal Integrability Problem for Planar Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, March.
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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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