Karma Dajani, Cor Kraaikamp, Wolfgang Steiner
Published 2007-02-18, updated 2008-02-25Version 2
The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. In this paper we introduce a new class of continued fractions related to the Rosen fractions, the $\alpha$-Rosen fractions. The metrical properties of these $\alpha$-Rosen fractions are studied. We find planar natural extensions for the associated interval maps, and show that these regions are closely related to similar region for the 'classical' Rosen fraction. This allows us to unify and generalize results of diophantine approximation from the literature.
On a theorem of V. Bernik in the metrical theory of Diophantine approximation
Metrical properties for the large partial quotients with product forms in continued fractions
On the Metrical Theory of a Generalized Continued Fraction Expansion
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