English
Multidimensional continued fractions and symbolic codings of toral translations
Virtualconference
Auteurs : Thuswaldner, Jörg (Auteur de la Conférence)
CIRM (Editeur )
11K50 - Metric theory of continued fractions
28A80 - Fractals
37A30 - Ergodic theorems, spectral theory, Markov operators
37B10 - Symbolic dynamics
CIRM (Editeur )
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Résumé :
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.
Keywords : toral rotation; continued fraction algorithm; Rauzy fractal
Codes MSC : Keywords : toral rotation; continued fraction algorithm; Rauzy fractal
11K50 - Metric theory of continued fractions
28A80 - Fractals
37A30 - Ergodic theorems, spectral theory, Markov operators
37B10 - Symbolic dynamics
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 24/11/2020 Sous collection : Research talks arXiv category : Dynamical Systems ; Number Theory Domaine : Combinatorics ; Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:57:17 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-24_Thuswaldner.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19689603Citer cette vidéo: Thuswaldner, Jörg (2020). Multidimensional continued fractions and symbolic codings of toral translations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19689603 URI : http://dx.doi.org/10.24350/CIRM.V.19689603 |
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Bibliographie
- 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
