The reversible context 2 in KAM theory: the first steps

The reversible context 2 in KAM theory refers to the situation where dim FixG < 1/2 codim T, here FixG is the fixed point manifold of the reversing involution G and 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.