Invariant tori for area-preserving maps with ultra-differentiable perturbation and Liouvillean frequency

Hongyu Cheng, Shimin Wang, Fenfen Wang

We prove the existence of invariant tori to the area-preserving maps defined on ${\mathbb{R}}^2\times \mathbb{T}$ \begin{equation*} \bar{x}=F(x,θ), \qquad \barθ=θ+α\, \,(α\in \mathb…