Nekhoroshev estimates for commuting nearly integrable symplectomorphisms

In this paper, we prove the Nekhoroshev estimates for commuting nearly integrable symplectomorphisms. We show quantitatively how ℤm 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.