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| Techniques of Nonautonomous Dynamics are applied to the study of the inverse spectral problem of the Sturm-Liouville eigenvalue equation $E\varphi:=-(p\varphi')'+q\varphi=\lambda y\varphi$ with $\lambda\in\mathbb C$ and potential $(p,q,y)$ belonging to a certain functional space. We focus on the problem of the construction and of the properties of potentials $(p,q,y)$ which are limits of the so-called algebro-geometric potentials. We also emphasize the relation between these potentials and the solutions of a hierarchy of highly nonlinear evolution equations. |
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