A Rauzy fractal unbounded in all directions of the plane
Mélodie Andrieu (Aix-Marseille University)
Abstract: Until 2001 it was believed that, as for Sturmian words, the imbalance of Arnoux-Rauzy words was bounded - or at least finite. Cassaigne, Ferenczi and Zamboni disproved this conjecture by constructing an Arnoux-Rauzy word with infinite imbalance, i.e. a word whose broken line deviates regularly and further and further from its average direction. Today, we hardly know anything about the geometrical and topological properties of these unbalanced Rauzy fractals. The Oseledets theorem suggests that these fractals are contained in a strip of the plane: indeed, if the Lyapunov exponents of the matricial product associated with the word exist, one of these exponents at least is nonpositive since their sum equals zero. This talk aims at disproving this belief.
dynamical systemsnumber theory
Audience: researchers in the topic
( slides )
Series comments: Description: Online seminar on numeration systems and related topics
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Organizers: | Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner* |
*contact for this listing |