A gauss-kuzmin theorem and related questions for $\theta$-expansions

Abstract

Using the natural extension for $\theta$-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

References in corpus (1)

• On a Gauss-Kuzmin-Type Problem for a Family of Continued Fraction Expansions

Cited by in corpus (4)

• Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions
• A Gauss-Kuzmin theorem for continued fractions associated with non-positive interger powers of an integer $m\ge 2$
• Metric properties of N-continued fractions
• A dependence with complete connections approach to generalized Rényi continued fractions