Journal
REGULAR & CHAOTIC DYNAMICS
Volume 21, Issue 6, Pages 599-620Publisher
PLEIADES PUBLISHING INC
DOI: 10.1134/S1560354716060022
Keywords
KAM theory; reversible systems; BCHV theorem; reversible context 2; invariant tori; Whitney smooth families
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We prove a general theorem on the persistence of Whitney C (a)-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.Hanmann, and A.Vanderbauwhede (2009) concerning quasi-periodic stability of invariant tori with singular normal matrices in reversible systems.
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