English
Rotated odometers
Virtualconference
Auteurs : Lukina, Olga (Auteur de la Conférence)
CIRM (Editeur )
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
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 : Keywords : infinite interval exchange transformation; Bratteli-Vershik system; flows on translation surfaces
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : 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 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic and Combinatorial Invariants of Subshifts and Tilings / Invariants combinatoires et algébriques des décalages et des pavagesOrganisateurs 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.19697303Citer 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
- [Multi angle] Interview au Cirm : Fabien Durand & Samuel Petite / Personne interviewée Durand, Fabien ; Personne interviewée Petite, Samuel.
- [Virtualconference] Nilpotent endomorphisms of expansive group actions / Auteur de la Conférence Salo, Ville.
- [Multi angle] Confined subgroups and high transitivity / Auteur de la Conférence Matte Bon, Nicolás.
- [Virtualconference] Number of ergodic and generic measures for minimal subshifts / Auteur de la Conférence Fickenscher, Jon.
- [Virtualconference] Recent developments in finite rank systems / Auteur de la Conférence Donoso, Sebastián.
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
