Codings of B-Integers in Cantor Numeration Systems as Generators of Aperiodic Potentials

Cantor real numeration systems provide a natural algebraic source of self-similar aperiodic structures, extending the classical β-integers framework introduced in quasicrystal modeling by Gazeau. We study how the choice of algebraic parameters of the base B=(βi)i∈Z influences the self-similarity and other combinatorial properties of the encoding symbolic sequence. These properties, namely repetitivity and palindromicity, are key features deciding the character of the spectrum of the underlying one-dimensional Schrödinger operator with aperiodic potential.