This article is cited 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.

MSC: 70K43, 70H33

Received: 09.05.2016
Accepted: 21.10.2016

Language: English

DOI: 10.1134/S1560354716060022

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