Quantum Birkhoff-Gustavson normal form in some completely resonant cases |
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| Authors: | Kaoutar Ghomari Bekkai Messirdi |
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| Institution: | a Department of Mathematics and Informatic, ENSET-Oran, Algeria
b Department of Mathematics, University of Oran, Algeria |
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| Abstract: | The goal of this paper is to present an explicit computation of the Birkhoff-Gustavson normal form in the 1:1, 1:2 and 1:3 resonances, by using the concept of Weyl quantization, especially when it is about the first terms. We use in particular the Weyl symbolic calculus and the abstract theorem of the quantum Birkhoff-Gustavson normal form in infinite dimension. |
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| Keywords: | Birkhoff normal form Harmonic oscillator Weyl quantization Resonances |
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