Multidimensional continued fractions and symbolic codings of toral translations | Vidéo | Carmin.tv

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Multidimensional continued fractions and symbolic codings of toral translations

By Jörg Thuswaldner

Appears in collection : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

The aim of this lecture is to find good symbolic codings for translations on the $d$-dimensional torus that enjoy the well-known and nice properties of Sturmian sequences (as for instance low complexity and good local discrepancy properties, i.e., bounded remainder sets of any scale). Inspired by the approach of G. Rauzy we construct such codings by the use of multidimensional continued fraction algorithms that are realized by sequences of substitutions. This is joint work with V. Berthé and W. Steiner.

Information about the video

Date of recording 24/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19689603
Cite this video Thuswaldner, Jörg (24/11/2020). Multidimensional continued fractions and symbolic codings of toral translations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19689603
URL https://dx.doi.org/10.24350/CIRM.V.19689603

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Bibliography

BERTHÉ, Valérie, STEINER, Wolfgang, et THUSWALDNER, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. arXiv preprint arXiv:2005.13038, 2020. - https://arxiv.org/abs/2005.13038

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