97-346 H. Schulz-Baldes, M. Zarrouati

Rigorous spectral analysis of the metal-insulator transition in a limit-periodic potential (121K, Postscript) Jun 17, 97

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Abstract. We consider the almost-periodic Jacobi matrices associated to the real Julia sets of $f_\lambda(z)=z^2-\lambda$ for which $\lambda\in [2,\infty)$ 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 $\lambda$ decreasing logarithmically from $1$ to $0$.

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