Concentration and non concentration for the Schrödinger equation on Zoll manifolds
Résumé
We study the long time dynamics of the Schrödinger equation on Zoll man-ifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate on a given closed geodesic. As an application, we derive some results on the set of semiclassical measures for eigenfunctions of Schrödinger operators: we prove that adding a potential to the Laplacian on the sphere results on the existence of geodesics $\gamma$ such that $\delta_{\Gamma}$ cannot be obtained as a semiclassical measure for some sequence of eigenfunctions. We also show that the same phenomenon occurs for the free Laplacian on certain Zoll surfaces.
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