| Abstract: |
| We study the discrete analytic Schr\odinger operator with a family of mappings. We first show that if the coupling number is large, then the Lyapunov exponent equals approximately to its logarithm. When applying it to the skew-shift mapping, we prove, that the Lyapunov exponent is positive and week H\older continuous, and the spectrum satisfies Anderson Localization and contains large intervals. Moreover, all of these conclusions for the skew shift Schr\odinger operator are non-perturbative. |
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