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Symplectic microgeometry II: generating functions


Cattaneo, A S; Dherin, B; Weinstein, A (2011). Symplectic microgeometry II: generating functions. Bulletin of the Brazilian Mathematical Society, N.S., 42(4):507-536.

Abstract

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.

Abstract

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of the temporal evolution in classical mechanics.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:08 Jan 2012 19:28
Last Modified:23 Nov 2017 07:19
Publisher:Springer
ISSN:1678-7544
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00574-011-0027-2
Related URLs:http://arxiv.org/abs/1103.0672

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