On periodic solutions of 2-periodic Lyness difference equations
Bastien, Guy (Université Paris. Institut Mathématique de Jussieu)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
Rogalski, Marc (Université de Lille(France). Laboratoire Paul Painlevé)

Date:	2013
Abstract:	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.
Grants:	Ministerio de Ciencia y Tecnología DPI2011-25822
Note:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Difference equations with periodic coefficients ; Elliptic curves ; Lyness' type equations ; QRT maps ; Rotation number ; Periodic orbits
Published in:	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

Postprint 27 p, 476.0 KB

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