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

Abstract

We consider a family $\{\tau_m:m\geq 2\}$ 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 Sz\"usz [18].