Iterations of homographic functions and recurrence equations involving a homographic function
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2015)
- Volume: 7, page 27-33
- ISSN: 2080-9751
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Abstract
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topJan Górowski, and Adam Łomnicki. "Iterations of homographic functions and recurrence equations involving a homographic function." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 7 (2015): 27-33. <http://eudml.org/doc/296336>.
@article{JanGórowski2015,
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},
author = {Jan Górowski, Adam Łomnicki},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {Iterations of homographic functions; recurrence equation; periodic sequences},
language = {pol},
pages = {27-33},
title = {Iterations of homographic functions and recurrence equations involving a homographic function},
url = {http://eudml.org/doc/296336},
volume = {7},
year = {2015},
}
TY - JOUR
AU - Jan Górowski
AU - Adam Łomnicki
TI - Iterations of homographic functions and recurrence equations involving a homographic function
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2015
VL - 7
SP - 27
EP - 33
AB - 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
LA - pol
KW - Iterations of homographic functions; recurrence equation; periodic sequences
UR - http://eudml.org/doc/296336
ER -
References
top- 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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