On periodic solutions of 2-periodic Lyness difference equations

Details On periodic solutions of 2-periodic Lyness difference equations On periodic solutions of 2-periodic Lyness difference equations

2012-01-04

arxiv.org/abs/1201.1027v1

Mathematics

Dynamical Systems

27 pages; 1 figure

Scientific paper

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_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) different from (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 is not equal to b, then any odd period, except 1, appears.

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