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UID:7480@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171006T100000
DTEND;TZID=Europe/Paris:20171006T160000
DTSTAMP:20241120T204342Z
URL:https://www.i2m.univ-amu.fr/evenements/geometry-dynamics-and-arithmeti
 c-of-s-adic-shifts/
SUMMARY:Jörg Thuswaldner (Montanuniversität Leoben\, Austria): Geometry\,
  dynamics\, and arithmetic of S-adic shifts
DESCRIPTION:Jörg Thuswaldner: This talk studies geometric and spectral pro
 perties of S-adic shifts and their relation to continued fraction algorith
 ms. These shifts are symbolic dynamical systems obtained by iterating infi
 nitely many substitutions. Pure discrete spectrum for S-adic shifts and ti
 ling properties of associated Rauzy fractals are established under a gener
 alized Pisot assumption together with a geometric coincidence condition. T
 hese general results extend the scope of the Pisot substitution conjecture
  to the S-adic framework. They are applied to families of S-adic shifts ge
 nerated by Arnoux-Rauzy as well as Brun substitutions. It is shown that al
 most all of these shifts have pure discrete spectrum. Using S-adic words r
 elated to Brun's continued fraction algorithm\, we exhibit bounded remaind
 er sets and natural codings for almost all translations on the two-dimensi
 onal torus. Due to the lack of self-similarity properties present for subs
 titutive systems we have to develop new proofs to obtain our results in th
 e S-adic setting.\nhttps://arxiv.org/abs/1410.0331\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 017/10/Joerg_Thuswaldner.jpg
CATEGORIES:Groupe de travail,Pythéas Fogg
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