29 citations · 64 across the 12 of their papers we have counts for
17 papers
The butterflies' effects
Siegfried Beckus
This work studies spectral properties of Schrödinger operators in the context of aperiodic order, using weighted Delone sets to explore the interplay between the underlying dynamic…
Spectral regularity and defects for the Kohmoto model
Siegfried Beckus, Jean Bellissard, Yannik Thomas
We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we…
Spectral estimates of dynamically-defined and amenable operator families
Siegfried Beckus, Alberto Takase
We consider kernel operators defined by a dynamical system. The Hausdorff distance of spectra is estimated by the Hausdorff distance of subsystems. We prove that the spectrum map i…
Symbolic substitution systems beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
In this article we construct the first examples of strongly aperiodic linearly repetitive Delone sets in non-abelian Lie groups by means of symbolic substitutions. In particular, w…
Growth of Eigenfunctions and R-limits on Graphs
Siegfried Beckus, Latif Eliaz
A characterization of the essential spectrum of Schrödinger operators on infinite graphs is derived involving the concept of -limits. This concept, whi…
Linear repetitivity beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weig…