Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori

TL;DR

This paper develops an abstract KAM theorem applicable to infinite-dimensional particle systems with long-range interactions, enabling the construction of full-dimensional invariant tori.

Contribution

It introduces a novel KAM framework for infinite particle systems with decay and all-to-all interactions, advancing the understanding of invariant structures in such systems.

Findings

Constructed full-dimensional KAM tori for infinite-dimensional systems.

Established an abstract KAM theorem for systems with decaying masses.

Extended KAM theory to long-range interacting particles.

Abstract

We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-dimensional KAM tori for infinite-dimensional mechanical systems exhibiting long range interactions.