On 2- and 3-periodic Lyness difference equations

We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of...

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Detalles Bibliográficos
Autores: Cimà, Anna|||0000-0003-0256-518X, Gasull, Armengol|||0000-0002-1719-8231, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150564
Acceso en línea:https://ddd.uab.cat/record/150564
https://dx.doi.org/urn:doi:10.1080/10236198.2010.524212
Access Level:acceso abierto
Palabra clave:Difference equations with periodic coefficients
Circle maps
Rotation number
Descripción
Sumario:We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.