Ergodic Properties Of $θ$-Expansions And A Gauss-Kuzmin-Type Problem

Abstract

A generalization of the regular continued fractions was given by Chakraborty and Rao \cite{CR-2003}. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For this expansion, we apply the method of Rockett and Szüsz \cite{RS-1992} and obtained the solution of its Gauss-Kuzmin-type problem.

19 pages