Global hypoelliptic vector fields in ultradifferentiable classes and normal forms

In this paper we prove that a global $omega$-hypoelliptic vector field on the torus $T^n$ can be transformed by a $mathcall{E}_omega}-diffeomorphism of $T^n$ into a vector field with constant coefficients which satisfy a Diophantine condition in terms of the weight function $omega$. Thereby, we extend previous work by Chen and Chi to a bigger scale of spaces, namely, in the setting of ultradifferentiable classes and ultradistributions of Beurling and Roumieu type.