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This article is cited in 10 scientific papers (total in 10 papers)
KAM theory for lower dimensional tori within the reversible context 2
Mikhail B. Sevryuk Institute of Energy Problems of Chemical Physics, The Russia Academy of Sciences, Leninskiĭ prospect 38, Bldg. 2, Moscow 119334, Russia
Abstract:
The reversible context 2 in KAM theory refers to the situation where $\mathrm{dim}\,\mathrm{Fix}\, G<\frac{1}{2}\mathrm{codim}\,\mathcal{T}$, here $\mathrm{Fix}\, G$ is the fixed point manifold of the reversing involution $G$ and $\mathcal{T}$ 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 $\mathrm{dim}\,\mathrm{Fix}\,G=0$ [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 $\mathrm{Fix}\, G$ is arbitrary. As in the case where $\mathrm{dim}\,\mathrm{Fix}\, G=0$, the main technical tool is J. Moser's modifying terms theorem of 1967.
Key words and phrases:
KAM theory, Moser's modifying terms theorem, reversible systems, reversible context 2, fixed point manifold, lower dimensional invariant torus.
Received: August 24, 2011
Citation:
Mikhail B. Sevryuk, “KAM theory for lower dimensional tori within the reversible context 2”, Mosc. Math. J., 12:2 (2012), 435–455
Linking options:
https://www.mathnet.ru/eng/mmj474 https://www.mathnet.ru/eng/mmj/v12/i2/p435
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Abstract page: | 159 | References: | 34 |
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