A proof of the invariant torus theorem of Kolmogorov

TL;DR

This paper provides a proof of Kolmogorov's invariant torus theorem utilizing a straightforward fixed point theorem, simplifying the understanding of the theorem's foundational aspects.

Contribution

It introduces a simplified proof of Kolmogorov's invariant torus theorem based on a basic fixed point theorem, enhancing conceptual clarity.

Findings

Proof confirms the existence of invariant tori under certain conditions

Simplifies the mathematical approach to Kolmogorov's theorem

Provides a new perspective on invariant torus existence

Abstract

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.