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.


39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
Full Text: DOI


[1] Cunningham, K.; Feuer, J.; Ladas, G.; Valicenti, S., On the difference equation xn+1=max{xn,A}/(xn2xn−1), () · 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 xn+1=max{xn,A}/(xnxn−1), J. comput. anal. appl., 2, 237-252, (2000) · Zbl 0958.39009
[4] Grove, E.A.; Janowski, E.J.; Kent, C.M.; Ladas, G., On the rational recursive sequence xn+1=αxn+β/((γxn+δ)xn−1), Commun. appl. nonlinear anal., 1, 61-72, (1994) · Zbl 0856.39011
[5] Kocic, V.L.; Ladas, G., Global behavior of nonlinear difference equations of higher order with applications, (1993), 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 xn+1=max{xn,A}/xn−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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.