Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant

TL;DR

This paper explores multi-Hamiltonian structures in Beauville's integrable system and its variant, connecting these findings to known Poisson structures on related systems, thereby advancing understanding of their geometric properties.

Contribution

It introduces a novel perspective on Beauville's system using multi-Hamiltonian structures and relates it to existing Poisson structures on Mumford systems.

Findings

Identification of multi-Hamiltonian structures on Beauville's system

Relation established between these structures and known Poisson structures

Enhanced understanding of the geometric framework of integrable systems

Abstract

We study Beauville's completely integrable system and its variant from a viewpoint of multi-Hamiltonian structures. We also relate our result to the previously known Poisson structures on the Mumford system and the even Mumford system.