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Natural extensions for the Rosen fractions |
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| Authors: | Robert M Burton Cornelis Kraaikamp Thomas A Schmidt |
| Institution: | Department of Mathematics, Oregon State University, Corvallis, Oregon 97331 ; Technische Universiteit Delft & Thomas Stieltjes Institute of Mathematics, ITS (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands ; Department of Mathematics, Oregon State University, Corvallis, Oregon 97331 |
| Abstract: | The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature. |
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