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

Fuzhong Cong; Hongtian Li

doi:10.3934/dcdsb.2015.20.1959

Article Contents

2015, Volume 20, Issue 7: 1959-1970. Doi: 10.3934/dcdsb.2015.20.1959

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

Fuzhong Cong^1, and
Hongtian Li^1,

1.
School of Mathematics, Jilin University, Changchun, 130012

Received: August 31, 2014

Revised: November 30, 2014

Published: August 2015

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Abstract

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.

Keywords:

Quasi-effective stability,
effective stability,
near-invariant torus,
nearly integrable volume-preserving mapping.

Mathematics Subject Classification: Primary: 37J40, 37E40, 37F50; Secondary: 65L20.

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