Some Remarks on Quantum Limits on Zoll Manifolds |
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Authors: | Fabricio Macià |
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Affiliation: | 1. Matemática Aplicada , Universidad Politécnica de Madrid , Madrid, Spain fabricio.macia@upm.es |
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Abstract: | We study the concentration of eigenfunctions of the Laplace–Beltrami operator on manifolds all whose geodesics are closed (the so-called Zoll manifolds). Some results on the structure of the set of invariant semiclassical measures associated to sequences of eigenfunctions are given. Among these, we show that any probability measure on the unit tangent bundle of a compact rank-one symmetric space that is invariant by the geodesic flow may be realized as the semiclassical measure of a sequence of eigenfunctions of the Laplacian. This extends a previous result of Jakobson and Zelditch on spheres. |
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Keywords: | Eigenfunction limits Integrable systems Quantum chaos Semiclassical measures |
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