S-expansions in dimension two

Bernhard Schratzberger[1]

  • [1] Universität Salzburg Institut für Mathematik Hellbrunnerstraße 34 5020 Salzburg, Austria

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 3, page 705-732
  • ISSN: 1246-7405

Abstract

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The technique of singularization was developped by C. Kraaikamp during the nineties, in connection with his work on dynamical systems related to continued fraction algorithms and their diophantine approximation properties. We generalize this technique from one into two dimensions. We apply the method to the the two dimensional Brun’s algorithm. We discuss, how this technique, and related ones, can be used to transfer certain metrical and diophantine properties from one algorithm to the others. In particular, we are interested in the transferability of the density of the invariant measure. Finally, we use this method to construct an algorithm which improves approximation properties, as opposed to Brun’s algorithm.

How to cite

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Schratzberger, Bernhard. "S-expansions in dimension two." Journal de Théorie des Nombres de Bordeaux 16.3 (2004): 705-732. <http://eudml.org/doc/249276>.

@article{Schratzberger2004,
abstract = {The technique of singularization was developped by C. Kraaikamp during the nineties, in connection with his work on dynamical systems related to continued fraction algorithms and their diophantine approximation properties. We generalize this technique from one into two dimensions. We apply the method to the the two dimensional Brun’s algorithm. We discuss, how this technique, and related ones, can be used to transfer certain metrical and diophantine properties from one algorithm to the others. In particular, we are interested in the transferability of the density of the invariant measure. Finally, we use this method to construct an algorithm which improves approximation properties, as opposed to Brun’s algorithm.},
affiliation = {Universität Salzburg Institut für Mathematik Hellbrunnerstraße 34 5020 Salzburg, Austria},
author = {Schratzberger, Bernhard},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {705-732},
publisher = {Université Bordeaux 1},
title = {S-expansions in dimension two},
url = {http://eudml.org/doc/249276},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Schratzberger, Bernhard
TI - S-expansions in dimension two
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 3
SP - 705
EP - 732
AB - The technique of singularization was developped by C. Kraaikamp during the nineties, in connection with his work on dynamical systems related to continued fraction algorithms and their diophantine approximation properties. We generalize this technique from one into two dimensions. We apply the method to the the two dimensional Brun’s algorithm. We discuss, how this technique, and related ones, can be used to transfer certain metrical and diophantine properties from one algorithm to the others. In particular, we are interested in the transferability of the density of the invariant measure. Finally, we use this method to construct an algorithm which improves approximation properties, as opposed to Brun’s algorithm.
LA - eng
UR - http://eudml.org/doc/249276
ER -

References

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