Abstract:

Motivated by the spectral analysis of Sturmian Hamiltonians, we investigate their underlying dynamical systems. This class of subshifts admits a natural extension to a larger family parameterized by the unit interval. In this talk, we study continuity properties of this parametrization with respect to the Hausdorff distance. Starting from the well known fact that these discontinuities arise at rational parameters only, we will pass to a non-Euclidean metric in order to characterize limits at rational parameters. If time permits we briefly discuss immediate implications for Sturmian Hamiltonians.

This talk is based on a joint work with Siegfried Beckus and Jean Bellissard.