Invariant hyperbolic tori for Hamiltonian systems with Rüssmann nondegeneracy conditions (Q1974418)
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scientific article; zbMATH DE number 1439637
| Language | Label | Description | Also known as |
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| English | Invariant hyperbolic tori for Hamiltonian systems with Rüssmann nondegeneracy conditions |
scientific article; zbMATH DE number 1439637 |
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Invariant hyperbolic tori for Hamiltonian systems with Rüssmann nondegeneracy conditions (English)
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23 November 2001
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The paper combines two known results in KAM theory, the result due to \textit{S. M. Graff} about the existence of hyperbolic tori for a perturbation of an integrable Hamiltonian system [J. Differ. Equations 15, 1-69 (1974; Zbl 0268.34051)], and that due to \textit{M. B. Sevryuk} [Dokl. Math. 53, No. 1, 69-72 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 346, 590-593 (1996; Zbl 0973.37035)] about the proof of the KAM theorem under the Rüssmann degeneracy condition ``the image of the frequency map does not belong to a hyperplane of the frequency space'', in other words, it proves Graff's result under the Rüssmann condition.
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integrable Hamiltonian system
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perturbation
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hyperbolic invariant tori
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Rüssmann degeneracy condition
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