Symplectic microgeometry II: generating functions

  • Alberto S. Cattaneo
  • Benoît Dherin
  • Alan Weinstein
Article

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.

Keywords

symplectic microfolds Hamilton-Jacobi canonical relations generating functions 

Mathematical subject classification

Primary: 53D05 Secondary: 70H15 

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Copyright information

© Springer 2011

Authors and Affiliations

  • Alberto S. Cattaneo
    • 1
  • Benoît Dherin
    • 2
  • Alan Weinstein
    • 3
  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Departamento de MatemáticaICMC-USPSão Carlos, SPBrazil
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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