Delone dynamical systems and spectral convergence
Abstract
In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on the autocorrelation, as well as on the density of states for random bounded operators. It is shown that for uniquely ergodic limit systems, the latter measures behave continuously with respect to the ChabautyFell convergence of hulls. In the special situation of Euclidean spaces, our results complement recent developments in describing spectra as topological limits: we show that the measured quantities under consideration can be approximated via periodic analogs.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.07644
 Bibcode:
 2017arXiv171107644B
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 34 pages