Properties of the nearest integer continued fraction expansions

Abstract

The nearest integer continued fraction of a real number $x$ from $[-1/2,1/2)$ is defined. Some metrical properties of these expansions are presented. We define the approximation coefficients and give an important result on them. The main result consists in obtaining a stationary state for the transformation ${\tau }_{1/2}$ which is absolutely continuous with respect to the Lebesgue measure.

This paper has been withdrawn