Continuous averaging proof of the Nekhoroshev theorem

TL;DR

This paper introduces a continuous averaging method to provide a new proof of the Nekhoroshev theorem, offering sharper estimates and explicit stability constants for long-term stability in Hamiltonian systems.

Contribution

It develops a novel continuous averaging approach for Nekhoroshev theorem proof, improving normal form results and stability estimates.

Findings

Sharp normal form theorem established

Explicit stability constants derived

Enhanced long-term stability estimates obtained

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