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Characterization of rational periodic sequences. II. (English) Zbl 1049.39003

[For part I see R. M. Abu-Sarris, ibid. 6, No. 2, 233–242 (2000; Zbl 0949.39002).]
Summary: We continue our investigation of the difference equation: \[ x_{n+1}=\frac{f(x_n)} {x_{n-1}} \] and characterize those functions for which all solutions of the above-mentioned difference equation are periodic of the same fundamental period \(p\). In particular, we address the cases \(p=3,4,5,6\).

MSC:

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

Citations:

Zbl 0949.39002
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References:

[1] Abu-Saris R, Far East J. Math. Scs. (FJMS) 1 pp 335– (1999)
[2] DOI: 10.1080/10236190008808223 · Zbl 0949.39002 · doi:10.1080/10236190008808223
[3] Abu-Saris R, J. Comp. Anal. Appl. 2 pp 103– (2000)
[4] Janowski EJ Kocic VL Ladas G Schultz SW Elaydi S Greaf J Ladas G Peterson A Global behavior of solutions of 273 282 1995
[5] DOI: 10.1007/978-94-017-1703-8 · doi:10.1007/978-94-017-1703-8
[6] Kulenovic M, Dynamics of Second Order Rational Difference Equations (2002)
[7] DOI: 10.1080/1023619031000061061 · Zbl 1030.39012 · doi:10.1080/1023619031000061061
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