Darboux normal form theorem as an example of Liouville integrability theorem

TL;DR

This paper presents a proof of Darboux and Liouville theorems using symplectic group actions, illustrating their connection to Liouville integrability in Hamiltonian systems.

Contribution

It provides a novel proof approach for classical theorems in symplectic geometry based on group actions, highlighting their role in integrability.

Findings

Proof of Darboux theorem via symplectic group actions

Proof of Liouville theorem via symplectic group actions

Clarification of the connection between symplectic symmetry and integrability

Abstract

The note offers a proof of Darboux and Liouville theorems from a symplectic group action perspective.