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On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\). (English) Zbl 1005.39016

The periodic character of solutions of the nonlinear difference equation \(x_{n+1}=-1/x_{n}+A/x_{n-1}\) is studied. It is shown that, if \(A\in (0,1],\) then every nonequilibrium solution to the above equation (which is well defined for all \(n\in \mathbb{N}\)) converges to the periodic solution \[ \dots ,-\sqrt{A+1},\;\sqrt{A+1},\;-\sqrt{A+1},\;\sqrt{A+1},\dots . \]

MSC:

39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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