The reversible context 2 in KAM theory: the first steps

The reversible context 2 in KAM theory refers to the situation where dim Fix $G < \frac{1}{2}$ codim $\mathcal{T}$, here Fix $G$ is the fixed point manifold of the reversing involution $G$ and $\mathcal{T}$ is the invariant torus one deals with. Up to now, this context has been entirely unexplored. We obtain a first result on the persistence of invariant tori in the reversible context 2 (for the particular case where dim Fix $G = 0$) using J. Moser’s modifying terms theorem of 1967.