On 2- and 3-periodic Lyness difference equations

Anna Cima, Armengol Gasull, Víctor Mañosa

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


We describe the sequences {x n} n given by the non-autonomous second-order Lyness difference equations x n+2 = (a n + x n+1)/x n, where {a n} n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x 1x 2 are also positive. We also show an interesting phenomenon of the discrete dynamical systems associated with some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behaviour does not appear for the autonomous Lyness difference equations. © 2012 Copyright Taylor and Francis Group, LLC.
Original languageEnglish
Pages (from-to)849-864
JournalJournal of Difference Equations and Applications
Issue number5
Publication statusPublished - 1 May 2012


  • circle maps
  • difference equations with periodic coefficients
  • rotation number


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