no. 2
A Gauss-Kuzmin theorem for the Rosen fractions
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.

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Sebe, Gabriela I. A Gauss-Kuzmin theorem for the Rosen fractions. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 667-682. http://www.numdam.org/item/JTNB_2002__14_2_667_0/

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