Moscow Mathematical Journal

Volume 17, Issue 4, October–December 2017 pp. 803–823.

Herman's Approach to Quasi-Periodic Perturbations in the Reversible KAM Context 2

Authors: Mikhail B. Sevryuk (1)
Author institution:(1) Talroze Institute of Energy Problems of Chemical Physics, The Russia Academy of Sciences, Leninskii prospect 38, Bldg. 2, Moscow 119334, Russia

Summary:

We revisit non-autonomous systems depending quasi-periodically in time within the reversible context 2 of KAM theory and obtain Whitney smooth families of invariant tori in such systems via Herman’s method. The reversible KAM context 2 refers to the situation where the dimension of the fixed point manifold of the reversing involution is less than half the codimension of the invariant torus in question.

2010 Math. Subj. Class. 70K43, 70H33.

Keywords: KAM theory, reversible context 2, Herman’s method, invariant tori, Whitney smooth families.

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