Geodesic
Iterative operators for Farey tree
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1.

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. 
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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},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2007},
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}
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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/