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We describe a numerical procedure to compute the so-called isospectral torusof finite gap sets, that is, the set of Jacobi matrices whose essentialspectrum is composed of finitely many intervals. We also study numerically theconvergence of specific Jacobi matrices to their isospectral limit. We thenextend the analyis to the definition and computation of an "isospectral torus"for Cantor sets in the family of Iterated Function Systems. This analysis isdeveloped with the ultimate goal of attacking numerically the conjecture thatthe Jacobi matrices of I.F.S. measures supported on Cantor sets areasymptotically almost-periodic.

Numerical computation of the isospectral torus of finite gap sets and of IFS Cantor sets