[Turkmath:7293] IMBM semineri - hatırlatma

[Muhammed Uludag]

I M B M Istanbul Center for Mathematical Sciences

*Self-similar Tilings and Local Rules.The Tribonacci Case.*
Xavier Bressaud, Toulouse University and Galatasaray University

Date: Thursday, November 4, 2010
Time: 15:00
Place: IMBM Seminar Room, Boğaziçi University

Abstract. The study of infinite words (symbolic dynamics) leads to
distinguish two particular classes of dynamical systems properties
dramatically different : substitutive systems (symbolic "self-similar"
systems) and subshifts of finite type (characterized by local rules).  This
distinction is deeply challenged in "size 2", that is to say for the study
of tilings of the plane, first by the existence of aperiodic tilings
characterized by certain local rules (Robinson) and by results of Moses and
Goodman-Strauss showing that large classes of "self-similar" tilings are
indeed characterized by local rules.
The self-similar tilings (quasicrystals) appearing in the study of symbolic
Pisot substitutions, particularly those representing discrete planes (with
quadratic slopes),
and more specifically the so-called Tribonacci tiling (aperiodic tiling by
Rauzy fractals)
are not covered by the result of Goodman-Strauss.

I will try to show how, using the same ideas, we can adapt existing results
for
characterizing Tribonacci tiling with local rules.
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