Quantum Birkhoff Normal Form in the $\sigma$-Bruno-Rüssmann non-resonant condition

Huanhuan Yuan, Yixian Gao, Yong Li

The aim of this paper is to construct a Gevrey quantum Birkhoff normal form for the $h$-differential operator $P_h(t),$ where $t\in (-\frac{1}{2},\frac{1}{2})$, in the neighborho…