Abstract
We study the global periodicity of difference equations of the form $% x_{n+1}=f(x_n)$, $x_{n+1}=f_n(x_n)$ and $x_{n+2}=f(x_n,x_{n+1})$. We characterize the $n$-cycles %%%(all the solutions of the equation is periodic with period at most $n$) in the case of first order equations and give some partial results for the second order equation. In particular, we find some examples of $3$-cycles which are different from the equation $x_{n+2}=\frac c{x_n x_{n+1}}$, solving a question of [2] and [4].
Citation
J. S. Cánovas. A. Linero Bas. G. Soler López. "ON GLOBAL PERIODICITY OF DIFFERENCE EQUATIONS." Taiwanese J. Math. 13 (6B) 1963 - 1983, 2009. https://doi.org/10.11650/twjm/1500405651
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