Periodic points of a Landen transformation

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 de...

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Detalles Bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Llorens, Mireia|||0000-0003-4710-8126, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:199367
Acceso en línea:https://ddd.uab.cat/record/199367
https://dx.doi.org/urn:doi:10.1016/j.cnsns.2018.04.020
Access Level:acceso abierto
Palabra clave:Landen transformation
Periodic points
Poincaré-Miranda theorem
Descripción
Sumario: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.