We continue the study of random continued fraction expansions, generated by application Gauss and Rényi backward maps. show that this dynamical system admits a unique absolutely continuous invariant measure with smooth density.

The study of combinatorial properties mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional fractions, which are generalization arising from an algorithm due to Jacobi, poorly investigated sense, up now. In paper, we propose interpretation the convergents terms counting some particular tilings, generaliz...