dc.contributor.author Bastien, Guy dc.contributor.author Mañosa Fernández, Víctor dc.contributor.author Rogalski, Marc dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III dc.date.accessioned 2012-01-10T08:45:03Z dc.date.available 2012-01-10T08:45:03Z dc.date.created 2012-01-04 dc.date.issued 2012-01-04 dc.identifier.citation Bastien, G.; Mañosa, V.; Rogalski, M. "On periodic solutions of 2-periodic Lyness difference equations". 2012. dc.identifier.uri http://hdl.handle.net/2117/14440 dc.description Preprint dc.description.abstract We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears. dc.format.extent 27 p. dc.language.iso eng dc.relation.ispartofseries arXiv:1201.1027v1 [math.DS] dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències dc.subject.lcsh Difference equations dc.subject.other Difference equations with periodic coefficients dc.subject.other Elliptic curves dc.subject.other Lyness' type equations dc.subject.other QRT maps dc.subject.other Rotation number dc.subject.other Periodic orbits dc.title On periodic solutions of 2-periodic Lyness difference equations dc.type Other dc.subject.lemac Equacions en diferències dc.contributor.group Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions dc.subject.ams Classificació AMS::39 Difference and functional equations::39A Difference equations dc.relation.publisherversion http://arxiv.org/abs/1201.1027 dc.rights.access Open Access drac.iddocument 8940413 dc.description.version Preprint upcommons.citation.author Bastien, G.; Mañosa, V.; Rogalski, M. upcommons.citation.published true upcommons.citation.publicationName On periodic solutions of 2-periodic Lyness difference equations
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