On the set of periods of the 2-periodic Lyness' equation

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/99190

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions
dc.contributor.author	Bastien, Guy
dc.contributor.author	Mañosa Fernández, Víctor
dc.contributor.author	Rogalski, Marc
dc.date	2012
dc.identifier.citation	Bastien, G., Mañosa, V., Rogalski, M. On the set of periods of the 2-periodic Lyness' equation. A: International Conference on Difference Equations and Applications. "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012". Barcelona: 2012, p. 321-335.
dc.identifier.citation	9783662529263
dc.identifier.citation	10.1007/978-3-662-52927-0_22
dc.identifier.uri	http://hdl.handle.net/2117/99190
dc.language.iso	eng
dc.relation	info:eu-repo/grantAgreement/ES/6PN/DPI2011-25822
dc.relation	info:eu-repo/grantAgreement/AGAUR/PRI2005-2008/2009SGR1228
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
dc.subject	Difference equations
dc.subject	Periodic orbits
dc.subject	Difference Equations
dc.subject	Ellipic curves
dc.subject	Lyness equations.
dc.subject	Equacions en diferències
dc.subject	Classificació AMS::39 Difference and functional equations::39A Difference equations
dc.title	On the set of periods of the 2-periodic Lyness' equation
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/conferenceObject
dc.description.abstract	The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-52927-0_22
dc.description.abstract	We study the periodic solutions of the non-autonomous periodic Lyness’ recurrence un+2=(an+un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a,b)¿(1,1), then there exists a value p0(a,b) such that for any p>p0(a,b) there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when (a,b)¿(0,8)2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a¿b, then it does not appear any odd period, except 1.
dc.description.abstract	Peer Reviewed

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