Ergodicity for [formula omitted]-adic continued fraction algorithms

Abstract

Following Schweiger’s generalization of multidimensional continued fraction algorithms, we consider a very large family of p-adic multidimensional continued fraction algorithms, which include Schneider’s algorithm, Ruban’s algorithms, and the p-adic Jacobi–Perron algorithm as special cases. The main result is to show that all the transformations in the family are ergodic with respect to the Haar measure.