Iterations of homographic functions and recurrence equations involving a homographic function

Jan Górowski, Adam Łomnicki


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


Iterations of homographic functions, recurrence equation, periodic sequences


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