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Arnold’s theorem on properly degenerate systems with the Rüssmann nondegeneracy

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Abstract

In this paper, we investigate the persistence of invariant tori for the nearly integrable Hamiltonian system \(H(x,y) = h(\hat y) + \varepsilon p(\hat x,y) + \varepsilon ^2 Q(x,y)\), where h(ŷ) and \(\varepsilon p(\hat x,y)\) satisfy the Rüssmann non-degenerate condition. Mainly we overcome the difficulties that the order of the parameter ε in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.

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Authors and Affiliations

  1. College of Mathematics, Jilin University, 130012, Changchun, China

    Han Yuecai & Li Yong

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  1. Han Yuecai
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  2. Li Yong
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Correspondence to Li Yong.

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Yuecai, H., Yong, L. Arnold’s theorem on properly degenerate systems with the Rüssmann nondegeneracy. Sci. China Ser. A-Math. 48, 1656–1669 (2005). https://doi.org/10.1360/022004-61

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  • DOI: https://doi.org/10.1360/022004-61

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