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- W577097669 abstract "We study the periodic solutions of the non-autonomous periodic Lyness’ recurrence $$u_{n+2}=(a_n+u_{n+1})/{u_n}$$ , where $${a_n}_n$$ 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 $$(a,b)ne (1,1)$$ , then there exists a value $$p_0(a,b)$$ such that for any $$p>p_0(a,b)$$ there exist continua of initial conditions giving rise to 2p-periodic sequences. (2) The set of minimal periods arising when $$(a,b)in (0,infty )^2$$ and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If $$ane b$$ , then it does not appear any odd period, except 1." @default.
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- W577097669 date "2016-01-01" @default.
- W577097669 modified "2023-10-18" @default.
- W577097669 title "On the Set of Periods of the 2-Periodic Lyness’ Equation" @default.
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- W577097669 doi "https://doi.org/10.1007/978-3-662-52927-0_22" @default.
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