24 citations · 56 across the 22 of their papers we have counts for
7 papers · 1 filter
Inducing contractions of the mother of all continued fractions
Karma Dajani, Cor Kraaikamp, Slade Sanderson
We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration te…
Approximation Results for alpha-Rosen Fractions
Cor Kraaikamp, Ionica Smeets
In this article we generalize Borel's classical approximation results for the regular continued fraction expansion to the alpha-Rosen fraction expansion, using a geometric method.…
Quilting natural extensions for alpha-Rosen Fractions
Cor Kraaikamp, Thomas A. Schmidt, Ionica Smeets
We give natural extensions for the alpha-Rosen continued fractions of Dajani et al. for a set of small alpha values by appropriately adding and deleting rectangles from the region…
Metric and arithmetic properties of mediant-Rosen maps
Cor Kraaikamp, Hitoshi Nakada, Thomas A. Schmidt
A continued fractions based verification of the Hurwitz values for the Hecke triangle groups is given, completing a program of Lehner's. Ergodic theory shows that Diophantine appro…
Sharp bounds for symmetric and asymmetric Diophantine approximation
Cor Kraaikamp, Ionica Smeets
In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next ap…
Tong's spectrum for Rosen continued fractions
Cor Kraaikamp, Thomas A. Schmidt, Ionica Smeets
The Rosen fractions are an infinite set of continued fraction algorithms, each giving expansions of real numbers in terms of certain algebraic integers. For each, we give a best po…
Metrical theory for -Rosen fractions
Karma Dajani, Cor Kraaikamp, Wolfgang Steiner
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…