LINEAR FRACTIONAL TRANSFORMATIONS OF CONTINUED FRACTIONS WITH BOUNDED PARTIAL QUOTIENTS IN THE FIELD OF FORMALSERIES

Abstract

Let θ be an irrational element in the field of formal series. Using a modification of the 1997 technique due to Lagarias and Shallit in the real numbers case, it is shown that if the continued fraction expansion of θ has bounded partial quotients, so does its linear fractional transformation.