On two and three periodic Lyness difference equations
Dynamical Systems
2013-07-26 v1
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.
Cite
@article{arxiv.0912.5031,
title = {On two and three periodic Lyness difference equations},
author = {Anna Cima and Armengol Gasull and Victor Manosa},
journal= {arXiv preprint arXiv:0912.5031},
year = {2013}
}
Comments
13 pages, 3 figures