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Periodic solutions of the Lyness max equation. (English) Zbl 1042.39002

The author considers the difference equation \(x_{n+1}= \max(x_n, A)/(x^l_n x_{n-1})\) with positive \(A\) and positive initial values in the two cases \(l=0\) and \(l=1\), respectively. He looks for periodic solutions and determines the possible periods.

MSC:

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

[1] Cunningham, K.; Feuer, J.; Ladas, G.; Valicenti, S., On the difference equation \(x_{n+1}=max{x_n,A}/(x_{n\) · Zbl 1062.39006
[2] Devaney, R., A piecewise linear model for the zones of instability of an area-preserving map, Phys. D, 10, 387-393 (1984) · Zbl 0588.58009
[3] Feuer, J.; Janowski, E. J.; Ladas, G.; Teixeira, C., Global behavior of solutions of \(x_{n+1}=max{x_n,A}/(x_{n\) · Zbl 0958.39009
[4] Grove, E. A.; Janowski, E. J.; Kent, C. M.; Ladas, G., On the rational recursive sequence \(x_{n+1}= αx_n+β/(( γx_n+δ)x_{n\)−1 · Zbl 0856.39011
[5] Kocic, V. L.; Ladas, G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0787.39001
[6] Kocic, V. L.; Ladas, G.; Rodrigues, I. W., On rational recursive sequences, J. Math. Anal. Appl., 173, 127-157 (1993) · Zbl 0777.39002
[7] Janowski, E. J.; Kocic, V. L.; Ladas, G.; Schultz, S. W., Global behavior of solutions of \(x_{n+1}=max{x_n,A}/x_{n\)−1 · Zbl 0860.39020
[8] Ladas, G., Invariants for generalized Lyness equations, J. Differ. Equations Appl., 1, 209-214 (1995) · Zbl 0858.39002
[9] Ladas, G., Open problems on the boundedness of some difference equations, J. Differ. Equations Appl., 1, 413-419 (1995) · Zbl 0853.39002
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