Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions
arXiv:1510.03606 · doi:10.1016/j.jmaa.2016.06.046
Abstract
We consider a family $\{T_N:N \geq 1 \}$ of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from $T_N$, we solve its Gauss-Kuzmin-type problem by applying the theory of random systems with complete connections by Iosifescu.
19 pages