Towards sharp regularity: Full-dimensional tori in $C^{\infty }$ vector fields over ${\mathbb{T}}^{\infty }$

Zhicheng Tong, Yong Li

We consider the $C^1$ linearization of a perturbed vector field $\omega +P$ over the infinite-dimensional torus ${\mathbb{T}}^{\infty }$, and determine the sharp regularity requirement…