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SUMMARY:Mélodie Andrieu (Aix-Marseille University)
DTSTART:20201027T133000Z
DTEND:20201027T143000Z
DTSTAMP:20260423T035605Z
UID:OWNS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/21/">A 
 Rauzy fractal unbounded in all directions of the plane</a>\nby Mélodie An
 drieu (Aix-Marseille University) as part of One World Numeration seminar\n
 \n\nAbstract\nUntil 2001 it was believed that\, as for Sturmian words\, th
 e imbalance of Arnoux-Rauzy words was bounded - or at least finite. Cassai
 gne\, Ferenczi and Zamboni disproved this conjecture by constructing an Ar
 noux-Rauzy word with infinite imbalance\, i.e. a word whose broken line de
 viates regularly and further and further from its average direction. Today
 \, we hardly know anything about the geometrical and topological propertie
 s of these unbalanced Rauzy fractals. The Oseledets theorem suggests that 
 these fractals are contained in a strip of the plane: indeed\, if the Lyap
 unov exponents of the matricial product associated with the word exist\, o
 ne of these exponents at least is nonpositive since their sum equals zero.
  This talk aims at disproving this belief.\n
LOCATION:https://researchseminars.org/talk/OWNS/21/
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