[Turkmath:7276] IMBM semineri

[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, Bo˘gazi¸ci 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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