A Gauss-Kuzmin theorem for the Rosen fractions
Gabriela I. Sebe
Journal de Théorie des Nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 667-682.

En utilisant les extensions naturelles des transformations de Rosen, nous obtenons une représentation de la chaîne d'ordre infini associée à la suite des quotients incomplets des fractions de Rosen. Associé au comportement ergodique d'un certain système aléatoire homogène à liaisons complètes, ce fait nous permet de résoudre une version du problème de Gauss-Kuzmin pour le développement en fraction de Rosen.

Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.

@article{JTNB_2002__14_2_667_0,
     author = {Sebe, Gabriela I.},
     title = {A {Gauss-Kuzmin} theorem for the {Rosen} fractions},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {667--682},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     doi = {10.5802/jtnb.381},
     zbl = {1067.11044},
     mrnumber = {2040700},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.381/}
}
Gabriela I. Sebe. A Gauss-Kuzmin theorem for the Rosen fractions. Journal de Théorie des Nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 667-682. doi : 10.5802/jtnb.381. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.381/

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