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A note on the periodicity of the Lyness max equation. (English) Zbl 1149.39004

Summary: We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is \(x_{n+1}= \max\{x_n,A\}/x_{n-1}\), where \(A\) is a positive real parameter, \(x-1=A^{r_{-1}}\), and \(x_0=A^{r_0}\) such that \(r_{-1}\) and \(r_0\) are positive rational numbers. The results in this paper answer the open problem of E. A. Grove and G. Ladas [Periodicities in nonlinear difference equation, Boca Raton (FL) (2005; Zbl 1078.39009)].

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations

Citations:

Zbl 1078.39009
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References:

[1] doi:10.1016/S0022-247X(03)00587-0 · Zbl 1042.39002
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