Speaker: Marta Dell ‘Atti

Title: Lagrangian multiform for finite dimensional systems

Abstract: Lagrangian multiforms provide a variational framework to describe integrable hierarchies, and the case of Lagrangian 1-forms covers finite-dimensional integrable systems. We use the theory of Lie di-algebras for r-matrices to construct a general Lagrangian 1-form. Given a Lie di-algebra associated with a Lie algebra and a collection of invariant functions $H_k$ under the group action, we give a formula for a Lagrangian multiform describing the commuting flows for $H_k$ on a coadjoint orbit. We focus on the open Toda chain by constructing two different Lie di-algebra structures and in both cases, we find a new set of canonical variables describing the chain for which we determine the relation with the Flaschka coordinates.