KAM Theorem and Renormalization Group

TL;DR

This paper provides an elementary proof of the analytic KAM theorem by connecting it to a PDE-based renormalization group approach from quantum field theory.

Contribution

It introduces a novel proof technique for the KAM theorem using a PDE and renormalization group framework, simplifying previous complex proofs.

Findings

Elementary proof of the KAM theorem

Reduction to a PDE with quadratic nonlinearity

Application of quantum field theory methods

Abstract

We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.