Metrical theory for -Rosen fractions

  • Cor Kraaikamp

    Delft University of Technology, Netherlands
  • Karma Dajani

    Universiteit Utrecht, Netherlands
  • Wolfgang Steiner

    Université Paris 7 Denis Diderot, France


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 α-Rosen fractions. The metrical properties of these α-Rosen fractions are studied.

We find planar natural extensions for the associated interval maps, and show that their domains of definition are closely related to the domains of the ‘classical’ Rosen fractions. This unifies and generalizes results of diophantine approximation from the literature.

Cite this article

Cor Kraaikamp, Karma Dajani, Wolfgang Steiner, Metrical theory for -Rosen fractions. J. Eur. Math. Soc. 11 (2009), no. 6, pp. 1259–1283

DOI 10.4171/JEMS/181