| Popis: |
Building on works of Berthe-Steiner-Thuswaldner and Fogg-Nous, we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence, we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrodinger operator has Cantor spectrum of zero Lebesgue measure. We also describe a framework that can allow this to be extended to higher-dimensional tori. |
