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 CMFD, 2017, Volume 63, Issue 3, Pages 516–541 (Mi cmfd333)

Partial preservation of frequencies and floquet exponents of invariant tori in the reversible KAM context 2

M. B. Sevryuk

V. L. Talroze Institute of Energy Problems of Chemical Physics of the Russia Academy of Sciences, 38 build. 2 Leninskii Prospect, 119334 Moscow, Russia

Abstract: We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions 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. The nondegeneracy conditions we employ ensure the preservation of any prescribed subsets of the frequencies of the unperturbed tori and of their Floquet exponents (the eigenvalues of the coefficient matrix of the variational equation along the torus).

DOI: https://doi.org/10.22363/2413-3639-2017-63-3-516-541

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UDC: 517.925.52

Citation: M. B. Sevryuk, “Partial preservation of frequencies and floquet exponents of invariant tori in the reversible KAM context 2”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 516–541

Citation in format AMSBIB
\Bibitem{Sev17} \by M.~B.~Sevryuk \paper Partial preservation of frequencies and floquet exponents of invariant tori in the reversible KAM context~2 \inbook Differential and functional differential equations \serial CMFD \yr 2017 \vol 63 \issue 3 \pages 516--541 \publ Peoples' Friendship University of Russia \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd333} \crossref{https://doi.org/10.22363/2413-3639-2017-63-3-516-541}