Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory

Abstract

We prove a general theorem on the persistence of Whitney infinitely smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where dim Fix G < (codim T)/2 where Fix G 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 of 2009 concerning quasi-periodic stability of invariant tori with singular "normal" matrices in reversible systems.