A lecture on the classical KAM theorem

TL;DR

This paper provides a clear, detailed explanation and proof of the classical KAM theorem, emphasizing the core ideas behind the theory rather than technical sharpness.

Contribution

It offers a comprehensive, accessible presentation of the classical KAM theorem with a complete proof following traditional methods.

Findings

Detailed proof of the classical KAM theorem

Emphasis on underlying ideas rather than technical sharpness

Clarification of the theorem's foundational concepts

Abstract

The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is more on the underlying ideas than on the sharpness of the arguments.