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

Key Points

• This research aims to explore how the parameters of Cantor numeration systems affect self-similar structures and their spectral properties.
• Analyzed algebraic parameters of base B in Cantor systems.
• Investigated the encoding symbolic sequences derived from β-integers.
• Examined properties like repetitivity and palindromicity.
• Studied the implications for the spectrum of the Schrödinger operator.
• Identified a direct relationship between algebraic parameters and self-similarity.
• Found variations in repetitivity and palindromicity linked to potential characteristics.
• Demonstrated that these properties influence the spectral behavior of the associated Schrödinger operator.

Abstract