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arXiv · 1103.0672

Symplectic Microgeometry II: Generating functions

Alberto S. Cattaneo·Benoit Dherin·Alan Weinstein
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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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Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein. 2011-03-03. Symplectic Microgeometry II: Generating functions. https://doi.org/10.1007/s00574-011-0027-2

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