Global periodicity and complete integrability of discrete dynamical systems

Anna Cima, Armengol Gasull, Víctor Mañosa

Research output: Contribution to journalArticleResearchpeer-review

25 Citations (Scopus)


Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F p(x) = x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations. © 2006 Taylor & Francis.
Original languageEnglish
Pages (from-to)697-716
JournalJournal of Difference Equations and Applications
Publication statusPublished - 1 Jan 2006


  • Completely integrable systems
  • Difference equations
  • First integrals
  • Globally periodic discrete dynamical system
  • Invariants for difference equations


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