# 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

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topSchratzberger, 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 -

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