Symplectic Microgeometry II: Generating functions

Details Symplectic Microgeometry II: Generating functions Symplectic Microgeometry II: Generating functions

2011-03-03

arxiv.org/abs/1103.0672v2

Mathematics

Symplectic Geometry

27 pages, 1 figure

Scientific paper

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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