Jean Morlet Chair - 2023 - Sem 2 - Athreya - Bédaride

Collection Jean Morlet Chair - 2023 - Sem 2 - Athreya - Bédaride

Organizer(s) Prof. Jayadev ATHREYA University of Washington & Nicolas BÉDARIDE Maître de Conférence Institut de Mathématiques de Marseille Aix-Marseille Université

Date(s) 01/07/2023 - 31/12/2023

linked URL https://www.chairejeanmorlet.com/2023-athreya-bedaride-2nd-semester.html

00:00:00 / 00:00:00

10 21

Renormalisation via continued fractions in symbolic dynamics

By Valérie Berthé

Also appears in collection : Jean Morlet Chair - Conference - Renormalization and Visualization in Geometry, Dynamics and number theory / Chaire Jean-Morlet - Conférence - Renormalisation et visualisation en géométrie, dynamique et théorie des nombres

We show how to construct 'simple' symbolic dynamical systems in terms of renormalisation schemes associated with multidimensional continued fractions. Continued fractions are used here to generate infinite words thanks to the iteration of infinite sequences of substitutions. Simple means that these symbolic systems have a linear number of factors of a given length, or that they have pure discrete spectrum, or else, that they have a low symbolic discrepancy. We also discuss the relation between these notions.

Information about the video

Date of recording 07/12/2023
Date of publication 22/12/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20116503
Cite this video Berthé, Valérie (07/12/2023). Renormalisation via continued fractions in symbolic dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20116503
URL https://dx.doi.org/10.24350/CIRM.V.20116503

Domain(s)

Dynamical Systems

Bibliography

BERTHÉ, Valérie, STEINER, Wolfgang, et THUSWALDNER, Jörg M. Multidimensional continued fractions and symbolic codings of toral translations. Journal of the European Mathematical Society, 2022, vol. 25, no 12, p. 4997-5057. - https://doi.org/10.4171/jems/1300

MSC codes

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