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On the Formal Integrability Problem for Planar Differential Systems

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  • Antonio Algaba
  • Cristóbal García
  • Jaume Giné

Abstract

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in , and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:482305
    DOI: 10.1155/2013/482305
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    Cited by:

    1. 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.
    2. Huang, Wentao & Gu, Tianlong & Li, Huili, 2014. "Integrability of fractional order generalized systems with p:-q resonance," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 82-86.
    3. 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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