Some remarks on the Classical KAM Theorem, following P{\"o}schel

TL;DR

This paper offers a minor correction and enhancement to Pöschel's classical KAM theorem, refining the understanding of invariant tori in Hamiltonian systems.

Contribution

It provides a subtle correction and improvement to Pöschel's main result on the classical KAM theorem.

Findings

Refined the conditions for the persistence of invariant tori.

Improved the mathematical precision of the KAM theorem.

Clarified aspects of Pöschel's original proof.

Abstract

We propose a slight correction and a slight improvement on the main result contained in "A lecture on Classical KAM Theorem" by J. P{\"o}schel.