dc.contributor.author |
Cimà, Anna |
dc.contributor.author |
Zafar, Sundus |
dc.date |
2014 |
dc.identifier |
https://ddd.uab.cat/record/150735 |
dc.identifier |
urn:10.1016/j.jmaa.2013.11.001 |
dc.identifier |
urn:oai:ddd.uab.cat:150735 |
dc.identifier |
urn:gsduab:3508 |
dc.identifier |
urn:scopus_id:84892858630 |
dc.identifier |
urn:wos_id:000330498900002 |
dc.identifier |
urn:oai:egreta.uab.cat:publications/a5c083dd-6a86-4693-bb93-e05f6d486a75 |
dc.identifier |
urn:articleid:10960813v413p20 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Ministerio de Ciencia y Tecnología MTM2008-03437 |
dc.relation |
Journal of mathematical analysis and applications ; Vol. 413 (2014), p. 20-34 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.title |
Integrability and algebraic entropy of k-periodic non-autonomous Lyness recurrences |
dc.type |
Article |
dc.description.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}. |