Geodesic
Iterations of homographic functions and recurrence equations involving a homographic function
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 7 (2015) no. 1, pp. 27-33

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The formulas for the m-th iterate (m ∈ 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 ∈ 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 
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Górowski, Jan; Łomnicki, Adam. Iterations of homographic functions and recurrence equations involving a homographic function. Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 7 (2015) no. 1, pp. 27-33. http://geodesic.mathdoc.fr/item/AUPCDM_2015_7_1_a1/