The KAM theorem through Dirichlet's box and Khintchine's transference principles

TL;DR

This paper presents a novel proof of the classical KAM theorem that circumvents small divisor issues by utilizing Dirichlet's box and Khintchine's transference principles from Diophantine approximation.

Contribution

The paper introduces a new proof of the KAM theorem based on Diophantine approximation principles, avoiding traditional small divisor techniques.

Findings

Proof avoids small divisor problems

Utilizes Dirichlet's box principle

Employs Khintchine transference principles

Abstract

In this paper, we give a new proof of the classical KAM theorem which avoids small divisors and relies on two basic principles of Diophantine approximation: Dirichlet's box and Khintchine transference principles.