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SUMMARY:Valérie Berthé (CNRS\, IRIF\, Université de Paris)
DTSTART:20210531T133000Z
DTEND:20210531T144500Z
DTSTAMP:20260423T021349Z
UID:BODS/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BODS/12/">Mu
 ltidimensional continued fractions and symbolic codings of toral translati
 ons</a>\nby Valérie Berthé (CNRS\, IRIF\, Université de Paris) as part 
 of Bremen Online Dynamics Seminar\n\n\nAbstract\nIt has been a long standi
 ng problem to find good symbolic codings for\nKronecker  toral  translatio
 ns  that enjoy the beautiful properties\nof Sturmian sequences like low fa
 ctor complexity and good local\ndiscrepancy properties. \nWe construct suc
 h codings in terms of multidimensional continued fraction\nalgorithms that
  are realized by sequences of substitutions. In particular\,\ngiven any st
 rongly convergent continued fraction algorithm\, these sequences\nlead to 
 renormalization schemes which produce symbolic codings and bounded\nremain
 der sets at all scales in a natural way.  Such sets \nprovide   particular
 ly strong convergence properties of  ergodic sums\, \nand are also  closel
 y related to the  notion of balance in word\ncombinatorics. \n As strong c
 onvergence of a continued fraction algorithm results in a Pisot\ntype prop
 erty\, our approach provides a systematic way to confirm purely\ndiscrete 
 \nspectrum results for wide classes of   substitutions.\nThis is joint wor
 k with W. Steiner and J. Thuswaldner.\n
LOCATION:https://researchseminars.org/talk/BODS/12/
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