Iterations of homographic functions and recurrence equations involving a homographic function

Abstract

The formulas for the $m$-th iterate $(m \in N)$ of an arbitrary homographicfunction $H$ are determined and the necessary and sufficient conditions for a solution ofthe equation $y_{m+1} = H(y_m)$, $m \in N$ to be an infinite $n$-periodic sequence are given. Based on the results from this paper one can easily determine some particular solutionsof the Babbage functional equation.