arXiv subjects
Publications and source records attributed to D. Damanik.
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive substitutions to minimal substitutions. This includes applications to random Schrödinger operators and to number theory.
We review the recent developments in the spectral theory of discrete one-dimensional Schrödinger operators with potentials generated by substitutions and circle maps. We discuss how occurrences of local repetitive structures allow for estimates of generalized eigenfunctions. Among the recent applications of this general approach are almost sure and uniform results on the absence of eigenvalues as well as continuity of the spectral measures with respect to Hausdorff measures.
We prove that a strong form of dynamical localization follows from a variable energy multi-scale analysis. This abstract result is applied to a number of models for wave propagation in disordered media.