Cotangent paths as coisotropic subsets for local functions
Résumé
We establish a local function version of a classical result claiming that a bivector field on a manifold M is Poisson if and only if cotan-gent paths form a coisotropic set of the infinite dimensional symplectic manifold of paths valued in T * M. Our purpose here is to prove this result without using the Banach manifold setting, setting which fails in the periodic case because cotangent loops do not form a Banach sub-manifold. Instead, we use local functions on the path space, a point of view that allows to speak of a coisotropic set.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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