On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\) (Q1599695)
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scientific article; zbMATH DE number 1751225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\) |
scientific article; zbMATH DE number 1751225 |
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On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\) (English)
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5 February 2003
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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 \[ \dots ,-\sqrt{A+1},\;\sqrt{A+1},\;-\sqrt{A+1},\;\sqrt{A+1},\dots . \]
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periodic solution
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asymptotic stability
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nonequilibrium solution
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