A semi-classical K.A.M. theorem

Details A semi-classical K.A.M. theorem A semi-classical K.A.M. theorem

2004-03-25

arxiv.org/abs/math-ph/0403045v2

Comm. Partial Differential Equations 32 (2007), no. 5, 745--770.

Physics

Mathematical Physics

One mistake in Proposition 15 corrected, introduction shortened, typographics errors fixed, bibliography updated

Scientific paper

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 $\hat{H}+\hbar^{\kappa}\hat{K}$, where $\hat{K}$ is an arbitrary pseudodifferential operator and $\kappa>0$, we prove the conjugacy to a suitable normal form. This is then used to construct a large number of quasimodes.

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