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Rotated odometers

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Virtualconference
Auteurs : Lukina, Olga (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : We consider infinite interval exchange transformations (IETs) obtained as a composition of a finite IET and the von Neumann-Kakutani map, called rotated odometers, and study their dynamical and ergodic properties by means of an associated Bratteli-Vershik system. We show that every rotated odometer is measurably isomorphic to the first return map of a rational parallel flow on a translation surface of finite area with infinite genus and a finite number of ends, with respect to the Lebesgue measure. This is one motivation for the study of rotated odometers. We also prove a few results about the factors of the unique minimal subsystem of a rotated odometer. This is joint work with Henk Bruin.

Keywords : infinite interval exchange transformation; Bratteli-Vershik system; flows on translation surfaces

Codes MSC :
28D05 - Measure-preserving transformations
37E05 - Maps of the interval (piecewise continuous, continuous, smooth)
37C83 - Dynamical systems with singularities (billiards, etc.)

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2313/Slides/Lukina-CIRM.pdf

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 26/01/2021
    Date de captation : 14/01/2021
    Sous collection : Research talks
    arXiv category : Dynamical Systems
    Domaine : Dynamical Systems & ODE ; Topology
    Format : MP4 (.mp4) - HD
    Durée : 01:02:37
    Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-01-14_Lukina.mp4

Informations sur la Rencontre

Nom de la rencontre : Algebraic and Combinatorial Invariants of Subshifts and Tilings / Invariants combinatoires et algébriques des décalages et des pavages
Organisateurs de la rencontre : Berthé, Valérie ; Cortez, Maria-Isabel ; Durand, Fabien ; Hosseini, Maryam ; Petite, Samuel
Dates : 11/01/2021 - 15/01/2021
Année de la rencontre : 2021
URL Congrès : https://conferences.cirm-math.fr/2313.html

Données de citation

DOI : 10.24350/CIRM.V.19697303
Citer cette vidéo: Lukina, Olga (2021). Rotated odometers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19697303
URI : http://dx.doi.org/10.24350/CIRM.V.19697303

Voir aussi

Bibliographie

  • BEZUGLYI, Sergey, KWIATKOWSKI, Jan, MEDYNETS, Konstantin, et al. Invariant measures on stationary Bratteli diagrams. Ergodic Theory and Dynamical Systems , Volume 30 , Issue 4 , August 2010 , pp. 973 - 1007 - https://doi.org/10.1017/S0143385709000443

  • CORTEZ, Maria Isabel, DURAND, Fabien, HOST, Bernard, et al. Continuous and measurable eigenfunctions of linearly recurrent dynamical Cantor systems. Journal of the London Mathematical Society, 2003, vol. 67, no 3, p. 790-804. - https://doi.org/10.1112/S0024610703004320

  • V. Delecroix, P. Hubert, F. Valdez, lnfinite translation surfaces in the wild, to appear. -

  • FERENCZI, Sébastien, MAUDUIT, Christian, et NOGUEIRA, Arnaldo. Substitution dynamical systems: algebraic characterization of eigenvalues. In : Annales scientifiques de l'Ecole normale supérieure. 1996. p. 519-533. - http://www.numdam.org/article/ASENS_1996_4_29_4_519_0.pdf

  • KEANE, Michael. Interval exchange transformations. Mathematische Zeitschrift, 1975, vol. 141, no 1, p. 25-31. - http://dx.doi.org/10.1007/BF01236981

  • RANDECKER, Anja. Geometry and topology of wild translation surfaces. KIT Scientific Publishing, 2016. - http://dx.doi.org/10.5445/KSP/1000050964



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