Generalized rational first integrals of analytic differential systems

Wang Cong, Jaume Llibre, Xiang Zhang

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17 Citations (Scopus)


In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincaré's one (Poincaré, 1891, 1897 [16]), the Furta's one (Furta, 1996 [8]), part of Chen et al.'s ones (Chen et al., 2008 [4]), and the Shi's one (Shi, 2007 [18]). The key point in the proof of our main results is that functionally independence of generalized rational functions implies the functionally independence of their lowest order rational homogeneous terms. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)2770-2788
JournalJournal of Differential Equations
Issue number10
Publication statusPublished - 15 Nov 2011


  • Differential systems
  • Generalized rational first integrals
  • Resonance


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