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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Symplectic microgeometry II: generating functions

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Author(s):
Cattaneo, Alberto S. [1] ; Dherin, Benoit [2] ; Weinstein, Alan [3]
Total Authors: 3
Affiliation:
[1] Univ Zurich, Inst Math, CH-8057 Zurich - Switzerland
[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 - USA
Total Affiliations: 3
Document type: Journal article
Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 42, n. 4, p. 507-536, DEC 2011.
Web of Science Citations: 8
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. (AU)

FAPESP's process: 10/15069-8 - Monoidal geometries
Grantee:Benoit Richard Umbert Dherin
Support Opportunities: Research Grants - Young Investigators Grants