Whitney smooth families of invariant tori within the reversible context 2 of KAM theory

We prove a general theorem on the persistence of Whitney C ^∞-smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where dim FixG < (codim T)/2, where FixG is the fixed point manifold of the reversing involution G and T is the invariant torus in question. Our result is obtained as a corollary of the theorem by H. W.Broer, M.-C.Ciocci, H.Hanßmann, and A.Vanderbauwhede (2009) concerning quasi-periodic stability of invariant tori with singular “normal” matrices in reversible systems.