KAM theory for lower dimensional tori within the reversible context 2

Details KAM theory for lower dimensional tori within the reversible context 2 KAM theory for lower dimensional tori within the reversible context 2

2011-08-30

arxiv.org/abs/1108.5975v1

Mathematics

Dynamical Systems

21 pages; dedicated to the memory of Vladimir Igorevich Arnold who is so unexpectedly gone

Scientific paper

The reversible context 2 in KAM theory refers to the situation where dim Fix G < (1/2) codim T, here Fix G is the fixed point manifold of the reversing involution G and T is the invariant torus one deals with. Up to now, the persistence of invariant tori in the reversible context 2 has been only explored in the extreme particular case where dim Fix G = 0 [M. B. Sevryuk, Regul. Chaotic Dyn. 16 (2011), no. 1-2, 24-38]. We obtain a KAM-type result for the reversible context 2 in the general situation where the dimension of Fix G is arbitrary. As in the case where dim Fix G = 0, the main technical tool is J. Moser's modifying terms theorem of 1967.

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