 9162 Obaya R., Paramio M.
 Directional Differentiability of the Rotation Number for the
Almost Periodic Schr\"{o}dinger Equation
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Nov 18, 91

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Abstract. Let us consider the onedimensional Schr\"{o}dinger equation
\begin{equation}\label{prim}
L_{E}(x)=x^{''}+g_0(t)xEx=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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