KAM theory at the Quantum resonance

Huanhuan Yuana, Yong Li

We consider the semiclassical operator $\hat{H}(\epsilon ,h):=H_0(h{D}_x)+\epsilon {\tilde{P}}_0$ on $L^2({\mathbb{R}}^l)$, where the symbol of $\hat{H}(\epsilon ,h)$ corresponds to a perturbed classi…