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UID:6321@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210928T110000
DTEND;TZID=Europe/Paris:20210928T120000
DTSTAMP:20241120T201402Z
URL:https://www.i2m.univ-amu.fr/evenements/natural-coding-of-minimal-rotat
 ions-of-the-torus-induction-and-exduction/
SUMMARY:Mélodie ANDRIEU (I2M\, Aix-Marseille Université): Natural coding 
 of minimal rotations of the torus\, induction and exduction
DESCRIPTION:Mélodie ANDRIEU: The notion of natural coding of rotation\, so
 metimes better called natural coding of translation of the torus\, goes ba
 ck to the works of Morse and Hedlund [MH40]\, and to the seed paper of Rau
 zy [Rau82] (study of the Tribonacci word) in dimension 2. Nonetheless\, th
 e terminology appears later (for instance in [CFZ01] and [Fog02]).\nRoughl
 y speaking\, a ”natural” coding of rotation denotes a word obtained as
  the coding trajectory of a point of the torus\, under the action of a rot
 ation\, with respect to a remarkable partition that can be covered such th
 at the induced rotation on the associated fundamental domain coincides\, o
 n each covered piece\, with a translation.\nAlthough much studied\, this n
 otion has never been well defined\; in particular\, there is no consensus 
 on the topological/metrical conditions that should satisfy the pieces of t
 he partition – without such conditions\, the definition is trivial.\nThe
  aim of this talk is to introduce a new topological definition\, with a mi
 nimal set of hypotheses.\nIn particular\, this definition should allow the
  study of words with infinite imbalance (like those constructed in [CFZ01]
 \, [DHS13] or in my thesis).\nShort references:\n[CFZ00] Cassaigne\, Feren
 czi\, Zamboni. “Imbalances in Arnoux-Rauzy sequences” (2000)\n[DHS13] 
 Delecroix\, Hejda\, Steiner. “Balancedness of Arnoux-Rauzy and Brun word
 s” (2013)\n[Fog02] Pytheas Fogg. “Substitutions in dynamics\, arithmet
 ics and combinatorics” (book\, 2002)\n[MH40] Morse and Hedlund. “Symbo
 lic dynamics ii. Sturmian trajectories” (1940)\n[Rau82] Rauzy. “Nombre
 s algébriques et substitutions” (1982)
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/03/Melodie_Andrieu.jpg
CATEGORIES:Séminaire,Ernest
LOCATION:Luminy\, Campus des Sciences de Luminy\, Marseille\, 13009\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus des Sciences de Lumi
 ny\, Marseille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy:geo:0,0
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