91-62 Obaya R., Paramio M.
Directional Differentiability of the Rotation Number for the Almost Periodic Schr\"{o}dinger Equation (87K, LaTeX) Nov 18, 91
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Abstract. Let us consider the one-dimensional Schr\"{o}dinger equation \begin{equation}\label{prim} L_{E}(x)=-x^{''}+g_0(t)x-Ex=0 \end{equation} with almost periodic potential $g_0$. The set $A$ of energies where the Lyapuo v exponent vanishes is also known to be the essential support of the absolutely continuous part of the spectral measure. This paper deals with the variation of the rotation number on $A$, in particular with the differentiability and Lipschitz character of this map.

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