## 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

### Keywords:

difference equation; periodic solutions
Full Text:

### References:

 [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
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