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Audiovisual Mathematics Library

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Rotated odometers

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Virtualconference
Authors : Lukina, Olga (Author of the conference)
CIRM (Publisher )

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Abstract : 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

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

Additional resources :
https://www.cirm-math.fr/RepOrga/2313/Slides/Lukina-CIRM.pdf
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 26/01/2021
    Conference Date : 14/01/2021
    Subseries : Research talks
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE ; Topology
    Format : MP4 (.mp4) - HD
    Video Time : 01:02:37
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2021-01-14_Lukina.mp4
Information on the Event

Event Title : Algebraic and Combinatorial Invariants of Subshifts and Tilings / Invariants combinatoires et algébriques des décalages et des pavages
Event Organizers : Berthé, Valérie ; Cortez, Maria-Isabel ; Durand, Fabien ; Hosseini, Maryam ; Petite, Samuel
Dates : 11/01/2021 - 15/01/2021
Event Year : 2021
Event URL : https://conferences.cirm-math.fr/2313.html

Citation Data

DOI : 10.24350/CIRM.V.19697303
Cite this video as: Lukina, Olga (2021). Rotated odometers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19697303
URI : http://dx.doi.org/10.24350/CIRM.V.19697303

See Also

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


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