Continuous averaging proof of the Nekhoroshev theorem

Jinxin Xue

doi:10.3934/dcds.2015.35.3827

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2015, Volume 35, Issue 8: 3827-3855. Doi: 10.3934/dcds.2015.35.3827

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Continuous averaging proof of the Nekhoroshev theorem

Jinxin Xue^1,

1.
Department of mathematics, the University of Chicago, Chicago, IL, 60637

Received: July 31, 2013

Revised: November 30, 2014

Published: May 2017

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Abstract

In this paper we develop the continuous averaging method of Treschev to work on the simultaneous Diophantine approximation and apply the result to give a new proof of the Nekhoroshev theorem. We obtain a sharp normal form theorem and explicit estimates of the stability constants appearing in the Nekhoroshev theorem.

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Mathematics Subject Classification: Primary: 37J40, 37J25; Secondary: 34D10.

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References

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