A decorated silver mean tiling with mixed spectrum

Franz Gähler
Universität Bielefeld

Date(s) : 06/03/2017   iCal
14 h 00 min - 15 h 00 min

Tilings generated by a primitive inflation give rise to a natural dynamical system, which acts by translations on their hull.
If the inflation factor is a Pisot number, the spectrum of this dynamical system has a non-trivial pure-point part, and the same holds true for the diffraction spectrum of the individual tilings.
There are conjectures, that under certain conditions all the spectrum is pure-point, but concrete examples with mixed spectrum in case those conditions are not satisfied are in fact rare. They typically are constant-length inflation tilings, which are equivalent a subshift.
In this talk, we present a method to construct examples with both a pure-point and a continuous part in the spectrum also when the inflation factor is an irrational Pisot number. An example based on the well-known silver mean tiling is then analysed in some detail.
This example is shown to have both a pure-point and a singular continuous spectral part.



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