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A semi-classical K.A.M. theorem

Nicolas Roy
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Abstract

We consider a semi-classical completely integrable system defined by a $\hbar$-pseudodifferential operator $\hat{H}$ on the torus $\mathbb{T}^{d}$. In order to study perturbed operators of the form $\hat{H}+\hbar^κ\hat{K}$, where $\hat{K}$ is an arbitrary pseudodifferential operator and $κ>0$, we prove the conjugacy to a suitable normal form. This is then used to construct a large number of quasimodes.

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Nicolas Roy. 2005-05-24. A semi-classical K.A.M. theorem. https://arxiv.org/abs/math-ph/0403045

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