Integrability and algebraic entropy of k-periodic non-autonomous Lyness recurrences
Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zafar, Sundus (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	This work deals with non-autonomous Lyness type recurrences of the form xn+2 = an + xn+1xn, where {an}n is a k-periodic sequence of positive numbers with minimal period k. We treat such non-autonomous recurrences via the autonomous dynamical system generated by the birational mapping Fak ◦ Fak−1 ◦ · · · ◦ Fa1 where Fa is defined by Fa(x, y) = (y,a+yx). For the cases k ∈ {1, 2, 3, 6} the corresponding mappings have a rational first integral. By calculating the dynamical degree we show that for k = 4 and for k = 5 generically the dynamical system in no longer rationally integrable. We also prove that the only values of k for which the corresponding dynamical system is rationally integrable for all the values of the involved parameters, are k ∈ {1, 2, 3, 6}.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Journal of mathematical analysis and applications, Vol. 413 (2014) , p. 20-34, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2013.11.001

Postprint 23 p, 408.0 KB

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