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Ergodic theory and discrete one-dimensional random Schrödinger operators: uniform existence of the Lyapunov exponent
[unknown]
2003
Contemporary Mathematics
unpublished
Preserved Fulltext
We review recent results which relate spectral theory of discrete one-dimensional Schrödinger operators over strictly ergodic systems to uniform existence of the Lyapunov exponent. In combination with suitable ergodic theorems this allows one to establish Cantor spectrum of Lebesgue measure zero for a large class of quasicrystal Schrödinger operators. The results can also be used to study non-uniformity of cocycles. While most part of the paper discuss already known results, we also include new
doi:10.1090/conm/327/05817
fatcat:53tmvmzlwjau5lytmcwivlq4qm