Nekhoroshev Estimates for Commuting Nearly Integrable Symplectomorphisms

    2017, Volume 22, Number 3, pp.  248-265

    Author(s): Xue J.

    In this paper, we prove the Nekhoroshev estimates for commuting nearly integrable symplectomorphisms. We show quantitatively how $\mathbb{Z}^m$ symmetry improves the stability time. This result can be considered as a counterpart of Moser’s theorem [11] on simultaneous
    conjugation of commuting circle maps in the context of Nekhoroshev stability. We also discuss the possibility of Tits’ alternative for nearly integrable symplectomorphisms.
    Keywords: Nekhoroshev estimates, commuting symplectomorphisms, generating functions, resonances
    Citation: Xue J., Nekhoroshev Estimates for Commuting Nearly Integrable Symplectomorphisms, Regular and Chaotic Dynamics, 2017, Volume 22, Number 3, pp. 248-265

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