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Quasi-effective stability for a nearly integrable volume-preserving mapping

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  • This paper is concerned with the stability of the orbits for a nearly integrable volume-preserving mapping. We prove that the nearly integrable volume-preserving mapping possesses quasi-effective stability under the classical KAM-type nondegeneracy, that is, there is an open subset of the phase space whose measure is nearly full, such that the considered mapping is effective stable on this subset. This announces a connection between the Nekhoroshev theory and KAM theory.
    Mathematics Subject Classification: Primary: 37J40, 37E40, 37F50; Secondary: 65L20.

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