Geodesic
Iterative operators for Farey tree
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1 
Ljubiša Kocić; Liljana Stefanovska; Sonja Gegovska-Zajkova. Iterative operators for Farey tree. Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1. http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a18/
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     author = {Ljubi\v{s}a Koci\'c and Liljana Stefanovska and Sonja Gegovska-Zajkova},
     title = {Iterative operators for {Farey} tree},
     journal = {Kragujevac Journal of Mathematics},
     pages = {253 - 262},
     year = {2007},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a18/}
}
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The existence of an operator that maps rational number $1/2$ into the array of Farey tree is proven. It is shown that this operator can be represented by combinatorial compositions of two simple real functions: $f:[0,\, 1]\rightarrow [1/2, \,1]$, which is $(0,\, 1)$-rational and $\sigma:[0,\, 1] \rightarrow [0,\, 1]$, which is linear. Then, another operator, mapping rational $r\in(0,\, 1)$ into the branch of the Farey tree emanating from the node characterized by $r$ is described.