Meromorphic first integrals of analytic diffeomorphisms

Armengol Gasull, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review


We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincaré type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.
Original languageEnglish
Article number126796
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Mar 2023


  • Discrete dynamical system
  • Integrability
  • Meromorphic first integrals


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