Modified Prüfer and Efgp Transforms and Deterministic Models with Dense Point Spectrum
نویسندگان
چکیده
We provide a new proof of the theorem of Simon and Zhu that in the region |E| < λ for a.e. energies, − d2 dx2 + λ cos(xα), 0 < α < 1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e. E ∈ [−2, 2] for the discrete model with V (j2) = ej , V (n) = 0 if n / ∈ {1, 4, 9, . . . }. The arguments depend on a direct analysis of the equations for the norm of a solution. §
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