Continuous averaging proof of the Nekhoroshev theorem

Jinxin Xue

Published 2012-10-15Version 1

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 an explicit estimate of the stability constants appearing in the Nekhoroshev theorem.