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arXiv · 0912.5031

On two and three periodic Lyness difference equations

Anna Cima·Armengol Gasull·Victor Manosa
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Abstract

We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x_1,x_2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.

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Anna Cima, Armengol Gasull, Victor Manosa. 2009-12-26. On two and three periodic Lyness difference equations. https://doi.org/10.1080/10236198.2010.524212

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