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On periodic solutions of 2-periodic Lyness difference equations
Bastien, Guy (Université Paris. Institut Mathématique de Jussieu)
Mañosa, Víctor (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
Rogalski, Marc (Université de Lille(France). Laboratoire Paul Painlevé)

Data: 2013
Resum: We study the existence of 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. 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) 6= (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 6= b, then any odd period, except 1, appears.
Nota: Número d'acord de subvenció MCYT/DPI2011-25822
Nota: Agraïments: CoDALab group is supported by the Catalonia’s government through the SGR program. The support of DMA3’s Terrassa Campus Section is also acknowledged.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Difference equations with periodic coefficients ; Elliptic curves ; Lyness’ type equations ; QRT maps ; Rotation number ; Periodic orbits
Publicat a: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 23 Núm. 4 (2013) , p. 1350071 (18 pages), ISSN 1793-6551

DOI: 10.1142/S0218127413500715

27 p, 476.0 KB

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