Complete integrability versus symmetry

TL;DR

This paper demonstrates that, on an open dense set, complete integrability in a system necessarily implies the presence of symmetry, highlighting a fundamental link between these concepts.

Contribution

It establishes a connection between complete integrability and symmetry, showing that integrability generally implies symmetry on a broad set.

Findings

Complete integrability implies symmetry on an open dense set.

The relationship between integrability and symmetry is fundamental in dynamical systems.

Symmetry is a consequence of integrability in most cases.

Abstract

The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.