Natural extensions for the Rosen fractions

Burton, Robert; Kraaikamp, Cornelis; Schmidt, Thomas

doi:10.1090/S0002-9947-99-02442-3

Natural extensions for the Rosen fractions
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by Robert M. Burton, Cornelis Kraaikamp and Thomas A. Schmidt PDF

Trans. Amer. Math. Soc. 352 (2000), 1277-1298 Request permission

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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