Diffieties and Liouvillian Systems

TL;DR

This paper introduces an alternative framework for Liouvillian systems using diffieties and infinite prolongation theory, expanding the understanding of systems that extend differential flatness and are prevalent in physics.

Contribution

It provides a new definition of Liouvillian systems through diffieties, bridging differential algebra and geometric approaches.

Findings

Liouvillian systems can be characterized using diffieties.

Many physical non-flat systems are Liouvillian.

The paper offers a geometric perspective on Liouvillian systems.

Abstract

Liouvillian systems were initially introduced within the framework of differential algebra. They can be seen as a natural extension of differential flat systems. Many physical non flat systems seem to be Liouvillian. We present in this paper an alternative definition to this class of systems using the language of diffieties and infinite prolongation theory.