On 2- and 3-periodic Lyness difference equations

We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial conditions x1; x2 are also positive. We also show an interesting phenomenon of t...

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Detalles Bibliográficos
Autores: Cima Mollet, Anna, Gasull Embid, Armengol, Mañosa Fernández, Víctor|||0000-0002-5082-3334
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/13175
Acceso en línea:https://hdl.handle.net/2117/13175
https://dx.doi.org/10.1080/10236198.2010.524212
Access Level:acceso abierto
Palabra clave:Difference equations
Difference equations with periodic coefficients
Circle maps
Rotation number
Equacions en diferències
Classificació AMS::39 Difference and functional equations::39A Difference equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
Descripción
Sumario:We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial conditions x1; x2 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