Numerical computation of the isospectral torus of finite gap sets and of IFS Cantor sets
This work provides numerical tools for studying spectral properties of Jacobi matrices associated with Cantor sets, which is a niche problem in mathematical physics and spectral theory.
The paper presents a numerical method to compute the isospectral torus for finite gap sets and extends it to Cantor sets from Iterated Function Systems, aiming to investigate the asymptotic almost-periodicity of Jacobi matrices for IFS measures.
We describe a numerical procedure to compute the so-called isospectral torus of finite gap sets, that is, the set of Jacobi matrices whose essential spectrum is composed of finitely many intervals. We also study numerically the convergence of specific Jacobi matrices to their isospectral limit. We then extend the analyis to the definition and computation of an "isospectral torus" for Cantor sets in the family of Iterated Function Systems. This analysis is developed with the ultimate goal of attacking numerically the conjecture that the Jacobi matrices of I.F.S. measures supported on Cantor sets are asymptotically almost-periodic.