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This article is cited in 5 scientific papers (total in 5 papers)
Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory
Mikhail B. Sevryuk V. L. Talroze Institute of Energy Problems of Chemical Physics
of the Russian Academy of Sciences,
Leninskii pr. 38, Building 2, Moscow, 119334 Russia
Abstract:
We prove a general theorem on the persistence of Whitney $C^\infty$-smooth families of invariant tori in the reversible
context 2 of KAM theory. This context refers to the situation where $\dim \text{Fix}\, G < (\text{codim}\mathcal{T})/2$, where $\text{Fix}\,G$ is the fixed point manifold of
the reversing involution $G$ and $\mathcal{T}$ 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 (2009) concerning quasi-periodic stability of invariant
tori with singular “normal” matrices in reversible systems.
Keywords:
KAM theory, reversible systems, BCHV theorem, reversible context 2, invariant tori, Whitney smooth families.
Received: 09.05.2016 Accepted: 21.10.2016
Citation:
Mikhail B. Sevryuk, “Whitney Smooth Families of Invariant Tori within the Reversible Context 2 of KAM Theory”, Regul. Chaotic Dyn., 21:6 (2016), 599–620
Linking options:
https://www.mathnet.ru/eng/rcd212 https://www.mathnet.ru/eng/rcd/v21/i6/p599
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Abstract page: | 121 | References: | 28 |
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