A Gauss-Kuzmin theorem for continued fractions associated with non-positive interger powers of an integer $m\ge 2$

Abstract

We consider a family $\{{\tau }_m:m\ge 2\}$ of interval maps introduced by Hei-Chi Chan [5] as generalizations of the Gauss transformation. For the continued fraction expansion arising from ${\tau }_m$, we solve its Gauss-Kuzmin-type problem by applying the method of Rockett and Szüsz [18].

18 pages

References in corpus (2)

• On a Gauss-Kuzmin-Type Problem for a Family of Continued Fraction Expansions
• A gauss-kuzmin theorem and related questions for $\theta$-expansions

Cited by in corpus (3)

• On certain generalizations of one function and related problems (Systems of functional equations and generalizations of certain functions)
• Ergodic Properties Of $\theta$-Expansions And A Gauss-Kuzmin-Type Problem
• Generalized Continued Logarithms and Related Continued Fractions