A gauss-kuzmin theorem and related questions for $θ$-expansions
arXiv:1305.5563 · doi:10.1155/2014/980461
Abstract
Using the natural extension for $θ$-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior 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.
27 pages