- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:06
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
6
Metrical theory for α-Rosen fractions
Karma
Dajani
Universiteit Utrecht, UTRECHT, NETHERLANDS
Cor
Kraaikamp
Delft University of Technology, CD DELFT, NETHERLANDS
Wolfgang
Steiner
Université Paris 7, Denis Diderot, PARIS CEDEX 05, FRANCE
Rosen fractions, natural extension, Diophantine approximation
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.
Number theory
General
1259
1283
10.4171/JEMS/181
http://www.ems-ph.org/doi/10.4171/JEMS/181