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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.

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  • 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
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  • 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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