### 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 1x 2 are also positive. We also show an interesting phenomenon of the discrete dynamical systems associated with some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behaviour does not appear for the autonomous Lyness difference equations. © 2012 Copyright Taylor and Francis Group, LLC.

Original language | English |
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Pages (from-to) | 849-864 |

Journal | Journal of Difference Equations and Applications |

Volume | 18 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 2012 |

### Keywords

- circle maps
- difference equations with periodic coefficients
- rotation number

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## Cite this

Cima, A., Gasull, A., & Mañosa, V. (2012). On 2- and 3-periodic Lyness difference equations.

*Journal of Difference Equations and Applications*,*18*(5), 849-864. https://doi.org/10.1080/10236198.2010.524212