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
Keywords
Iterations of homographic functions, recurrence equation, periodic sequences
References
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Wachniccy, K. E.: 1966, O ciągach rekurencyjnych określonych funkcją homograficzną, Gradient 5, 275-288.
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