Reduction and Integrability

TL;DR

This paper explores how the integrability of a dynamical system with symmetry relates to the integrability of its reduced form, providing insights into the structure of such systems.

Contribution

It establishes a connection between the integrability of a system and its reduction under Lie group actions, advancing understanding of symmetry and integrability.

Findings

Reduced systems inherit integrability properties under certain conditions

Conditions for integrability transfer between original and reduced systems

Framework for analyzing integrability in symmetric dynamical systems

Abstract

We discuss the relationship between the integrability of a dynamical system invariant under a Lie group action and its reduced integrability, i.e. integrability of the corresponding reduced system.