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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 ℂ2, 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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:482305
    DOI: 10.1155/2013/482305
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    References listed on IDEAS

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    1. Algaba, A. & García, C. & Reyes, M., 2012. "Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 869-878.
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