On the set of periods of the 2-periodic Lyness' equation
Bastien, Guy (Université Pierre et Marie Curie)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Rogalski, Marc (Université des Sciences et Technologies de Lille)

Imprint:	Cham, Switzerland: Springer, 2016
Description:	14 pàg.
Abstract:	We study the periodic solutions of the non-autonomous periodic Lyness' recurrence u = (a + u )/u, where {a} 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 p(a, b) such that for any p > p(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,∞) 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.
Grants:	Ministerio de Economía y Competitividad DPI2011-25822 Ministerio de Economía y Competitividad DPI2016-77407-P
Note:	Publicació amb motiu de la International Conference on Difference Equations and Applications (July 22-27, 2012, Barcelona, Spain) amb el títol Difference Equations, Discrete Dynamical Systems and Applications
Rights:	Tots els drets reservats.
Language:	Anglès
Series:	Springer Proceedings in Mathematics & Statistics ; 180
Document:	Capítol de llibre ; recerca ; Versió acceptada per publicar
Subject:	Difference equations with periodic coefficients ; Elliptic curves ; Lyness' type equations ; QRT maps ; Rotation number ; Periodic orbits
Published in:	IDifference Equations, Discrete Dynamical Systems and Applications, 2016, p. 321-335, ISBN 978-3-662-52927-0

DOI: 10.1007/978-3-662-52927-0_22

Postprint 14 p, 253.9 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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