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High energy distribution of eigenstates for small perturbations of completely integrable systems

Victor Arnaiz Solórzano
Tuesday, November 5, 2019 - 14:00 to 16:00

In the first lecture of this seminar, I will give you  an introduction to semiclassical analysis, concerning basic tools of  pseudodifferential calculus, quantum limits, semiclassical measures,  construction of quasimodes, and related topics. We will pay special  attention to  some well establish examples of completely integrable  systems to exercise the tools and ideas introduced.

In the second lecture, I will present you some new results concerning  the semiclassical limit of sequences of eigenfunctions for small  perturbations of completely integrable systems. To deep in the proofs,  we will use some of the tools introduced in the first talk together  with some KAM techniques.

Part of this work has been obtained in collaboration with Fabricio Macià.

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