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https://open.uns.ac.rs/handle/123456789/5453
Title: | A regularization approach to non-smooth symplectic geometry | Authors: | Hörmann G. Konjik, Sanja Kunzinger M. |
Issue Date: | 1-Jan-2015 | Journal: | Operator Theory: Advances and Applications | Abstract: | © 2015 Springer International Publishing Switzerland. 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 nonsmooth 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. | URI: | https://open.uns.ac.rs/handle/123456789/5453 | ISSN: | 02550156 |
Appears in Collections: | PMF Publikacije/Publications |
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