Symplectic Microgeometry II: Generating functions
  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. 
Alberto S. Cattaneo, Benoit Dherin and Alan Weinstein
math.SG math-ph math.MP