Abstract |
Sturmian sequences provide prototypical mathematical models for one
dimensional quasicrystals. Regularity properties of these sequences are
well understood, thanks mostly to foundational results of Morse and
Hedlund, and physicists have used this understanding to study random
Schrodinger operators and lattice gas models for one dimensional
quasicrystals. A fact which plays an important role in these problems is
the existence of a subadditive ergodic theorem, which is guaranteed when
the corresponding point set is linearly repetitive. In this talk we will
explain an effort to extend the one dimensional model to cut and project
sets, which generalize Sturmian sequences in higher dimensions, and which
are frequently used in mathematical and physical literature as models for
higher dimensional quasicrystals. Most of the above concepts and
terminology will be defined in the talk, only basic knowledge of analysis
and dynamical systems will be supposed.
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