Hidden Singularity and Fractal Dimensions for Extended Harper Operators
This paper establishes that the spectra of extended Harper operators in the zero-measure regime possess finite -dimensional Hausdorff measure and a lower box dimension of at most (improving to on the isotropic critical boundary) by utilizing a family of unitary transformations to map these operators to singular Jacobi representatives, thereby enabling the construction of specific interval covers that yield these fractal dimension bounds and demonstrate cases where the box-counting dimension fails to exist.