Constructive gap-labelling and scaling properties of the Fibonacci Hamiltonian

22.01.2025, 13:00  –  Haus 9, Raum 2.22 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Laurent Raymond (Marseille)

Abstract: With the recent publication of a solution of the the so-called « dry ten martinis problem », closing an old conjecture about the gap-labeling of of calls of aperiodic Schrödinger operators (with sturmian potential), it could be of some interest to give a review on the starting point of the « constructive » version of the gap-labeling theorem. I will present this construction in the simplest case (Fibonacci sequence) for which one also gets a useful estimate of the scaling properties leading to bounds on the fractal dimension of the spectrum of this operator.