En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Multidimensional continued fractions and symbolic codings of toral translations

Bookmarks Report an error
Virtualconference
Authors : Thuswaldner, Jörg (Author of the conference)
CIRM (Publisher )

Loading the player...

Abstract : 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

MSC Codes :
11K50 - Metric theory of continued fractions
28A80 - Fractals
37A30 - Ergodic theorems, spectral theory, Markov operators
37B10 - Symbolic dynamics

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 01/12/2020
    Conference Date : 24/11/2020
    Subseries : Research talks
    arXiv category : Dynamical Systems ; Number Theory
    Mathematical Area(s) : Combinatorics ; Dynamical Systems & ODE ; Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 00:57:17
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2020-11-24_Thuswaldner.mp4

Information on the Event

Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire
Event Organizers : Rivat, Joël ; Tichy, Robert
Dates : 23/11/2020 - 27/11/2020
Event Year : 2020
Event URL : https://www.chairejeanmorlet.com/2256.html

Citation Data

DOI : 10.24350/CIRM.V.19689603
Cite this video as: 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

See Also

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



Bookmarks Report an error