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Spectral stability and semiclassical measures for renormalized KAM systems

Mathematical Physics 2020-09-30 v5 Analysis of PDEs Dynamical Systems math.MP

Abstract

An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being completely integrable is obtained. We apply these results to characterize the sets of semiclassical measures and quantum limits for sequences of L2L^2-eigenfunctions of these systems.

Keywords

Cite

@article{arxiv.1811.12300,
  title  = {Spectral stability and semiclassical measures for renormalized KAM systems},
  author = {Victor Arnaiz},
  journal= {arXiv preprint arXiv:1811.12300},
  year   = {2020}
}

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26 pages