Rotated odometers | Vidéo | Carmin.tv

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Rotated odometers

Appears in collection : Algebraic and Combinatorial Invariants of Subshifts and Tilings / Invariants combinatoires et algébriques des décalages et des pavages

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.

Information about the video

Date of recording 14/01/2021
Date of publication 26/01/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19697303
Cite this video Lukina, Olga (14/01/2021). Rotated odometers. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19697303
URL https://dx.doi.org/10.24350/CIRM.V.19697303

Domain(s)

Dynamical Systems

Bibliography

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

MSC codes

Document(s)

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

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