Geodesic
On topological properties of manifolds of eigenfunctions generated by a~family of periodic Sturm--Liouville problems
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 22-37

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In the paper, we study manifolds of eigenfunctions of a fixed oscillation. Then, solving the trivial inverse problem of reconstruction of a potential by an eigenfunction, we describe the properties of manifolds of potentials. The approach proposed allows one to link topological properties of manifolds of eigenfunctions with those of manifolds of potentials. 
@article{CMFD_2006_16_a2,
     author = {Ya. M. Dymarskii},
     title = {On topological properties of manifolds of eigenfunctions generated by a~family of periodic {Sturm--Liouville} problems},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {22--37},
     publisher = {mathdoc},
     volume = {16},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_16_a2/}
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Ya. M. Dymarskii. On topological properties of manifolds of eigenfunctions generated by a~family of periodic Sturm--Liouville problems. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 22-37. http://geodesic.mathdoc.fr/item/CMFD_2006_16_a2/