A Gauss-Kuzmin Theorem and Related Questions for θ-Expansions

الملخص EN

Using the natural extension for θ-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotientsof these expansions.

Together with the ergodic behavior of a certainhomogeneous random system with complete connections, this allowsus to solve a variant of Gauss-Kuzmin problem for the previous fraction expansion.