On the oscillation and periodic character of a third order rational difference equation

Patula, W.; Voulov, H.

doi:10.1090/S0002-9939-02-06611-X

On the oscillation and periodic character of a third order rational difference equation
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by W. T. Patula and H. D. Voulov PDF

Proc. Amer. Math. Soc. 131 (2003), 905-909 Request permission

Abstract:

We prove that every positive solution of the following difference equation: \[ x_n = 1 + \frac {x_{n-2}}{x_{n-3}}, \quad n = 0,1,\ldots , \] converges to a period two solution.

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