KAM theorem for reversible mapping of low smoothness with application

Jing Li, Jiangang Qi, Xiaoping Yuan

Assume the mapping $$A:\{\begin{array}{l}{x}_1=x+\omega +y+f(x,y),y_1=y+g(x,y),\end{array}(x,y)\in {\mathbb{T}}^d\times B(r_0)$$ is reversible with respect to $G…