A regularization approach to non-smooth symplectic geometry

Autor:	Hoermann, Guenther, Konjik, Sanja, Kunzinger, Michael
Rok vydání:	2014
Předmět:	Mathematics - Differential Geometry 53D05 46F30
Zdroj:	Pseudo-differential operators and generalized functions, 119-132, Oper. Theory Adv. Appl., 245, Birkhaeuser, Springer, Cham, 2015
Druh dokumentu:	Working Paper
Popis:	We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to Hamiltonian vector fields to the setting of non-smooth geometry. For mildly singular symplectic forms, including the continuous non-differentiable case, we prove the existence of generalized Darboux coordinates in the sense of a local non-smooth pull-back to the canonical symplectic form on the cotangent bundle. Comment: 12 pages, final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1403.0234 Zobrazit plný text záznamu View this record from Arxiv