Iterations of homographic functions and recurrence equations involving a homographic function

Authors

  • Jan Górowski Instytut Matematyki Uniwersytet Pedagogiczny w Krakowie, ul. Podchorążych 2, 30-084 Kraków
  • Adam Łomnicki Instytut Matematyki Uniwersytet Pedagogiczny w Krakowie, ul. Podchorążych 2, 30-084 Kraków

Keywords:

Iterations of homographic functions, recurrence equation, periodic sequences

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

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References

Graham, R. L., Knuth, D. E., Patashnik, O.: 2002, Matematyka konkretna, PWN, Warszawa.

Koźniewska, J.: 1972, Równania rekurencyjne, PWN, Warszawa.

Kuczma, M.: 1968, Functional Equations in a Single Variable, Monogr. Math. 46, PWN Polish Scientific Publishers, Warszawa.

Levy, H., Lessman, F.: 1966, Równania różnicowe skończone, PWN, Warszawa.

Uss, P.: 1966, Rekurencyjność inaczej, Gradient 2, 102-106.

Wachniccy, K. E.: 1966, O ciągach rekurencyjnych określonych funkcją homograficzną, Gradient 5, 275-288.

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Published

2017-07-04

How to Cite

Górowski, J., & Łomnicki, A. (2017). Iterations of homographic functions and recurrence equations involving a homographic function. Annales Universitatis Paedagogicae Cracoviensis | Studia Ad Didacticam Mathematicae Pertinentia, 7, 27–33. Retrieved from https://didacticammath.uken.krakow.pl/article/view/3625

Issue

Vol. 7 (2015)

Section

Contents

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