Lior Tenenbaum (Potsdam)

In studying higher dimensional Schrödinger operators of quasicrystals, one is lead to find suitable periodic approximations. This means in particular that the spectrum converges as a set to the limiting spectrum. It turns out that the convergence of the underlying dynamical systems is exactly what one needs to do so. This is the starting point of the present talk. We treat subshifts defined through so-called substitutions. These subshifts provide models of aperiodic ordered systems. We find natural sequences of subshifts converging to the substitution subshift.  Some well-known examples of substitution subshifts are discussed during the talk. We will also discuss the motivation for this characterization, arising from an attempt to study higher dimensional quasi-crystals.
This is based on a Joint work with Ram Band, Siegfried Beckus and Felix Pogorzelski.
_{Contact: Daniel Lenz}