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Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition

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Abstract

In this paper, we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Rüssmann’s non-degeneracy condition by an improved KAM iteration, and the persisting invariant tori are Gevrey smooth, with the same Gevrey index as the Hamiltonian.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, P. R. China

    Dong Feng Zhang & Jun Xiang Xu

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  1. Dong Feng Zhang
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  2. Jun Xiang Xu
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Correspondence to Dong Feng Zhang.

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Project 10571027 supported by NSFC

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Zhang, D.F., Xu, J.X. Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition. Acta. Math. Sin.-English Ser. 24, 1625–1636 (2008). https://doi.org/10.1007/s10114-008-6180-x

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  • DOI: https://doi.org/10.1007/s10114-008-6180-x

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