Abstract
We consider the limit-periodic Jacobi matrices associated with the real Julia sets of f λ(z)=z 2−λ for which λ∈[2, ∞) can be seen as the strength of the limit-periodic coefficients. The typical local spectral exponent of their spectral measures is shown to be a harmonic function in λ decreasing logarithmically from 1 to 0.
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Schulz-Baldes, H., Zarrouati, M. Rigorous Spectral Analysis of the Metal–Insulator Transition in a Limit-Periodic Potential. Journal of Statistical Physics 91, 801–806 (1998). https://doi.org/10.1023/A:1023094030969
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DOI: https://doi.org/10.1023/A:1023094030969