Local first integrals of differential systems and diffeomorphisms

Weigu Li, Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

40 Citations (Scopus)


In this paper using theory of linear operators and normal forms we generalize a result of Poincaré about the non-existence of local first integrals for systems of differential equations in a neighbourhood of a singular point. As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semi-quasi-homogeneous systems. Moreover, for diffeomorphisms and periodic differential systems we give definitions of their first integrals, and generalize the previous results about systems of differential equations to diffeomorphisms in a neighbourhood of a fixed point and to periodic differential systems in a neighbourhood of a constant solution.
Original languageEnglish
Pages (from-to)235-255
JournalZeitschrift fur Angewandte Mathematik und Physik
Publication statusPublished - 1 Mar 2003


  • Diffeomorphism
  • Differential system
  • Local first integral
  • Normal form


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