Periodic points of a Landen transformation

Armengol Gasull, Mireia Llorens, Víctor Mañosa

Research output: Contribution to journalArticleResearch

4 Citations (Scopus)


© 2018 Elsevier B.V. We prove the existence of 3-periodic orbits in a dynamical system associated to a Landen transformation previously studied by Boros, Chamberland and Moll, disproving a conjecture on the dynamics of this planar map introduced by the latter author. To this end we present a systematic methodology to determine and locate analytically isolated periodic points of algebraic maps. This approach can be useful to study other discrete dynamical systems with algebraic nature. Complementary results on the dynamics of the map associated with the Landen transformation are also presented.
Original languageEnglish
Pages (from-to)232-245
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - 1 Nov 2018


  • Landen transformation
  • Periodic points
  • Poincaré–Miranda theorem


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