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Symplectic microgeometry II: generating functions

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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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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Alberto S. Cattaneo

  2. Departamento de Matemática, ICMC-USP, Av. do Trabalhador São Carlense, 400, Centro, 13560-970, São Carlos, SP, Brazil

    Benoît Dherin

  3. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Alan Weinstein

Authors
  1. Alberto S. Cattaneo
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  2. Benoît Dherin
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  3. Alan Weinstein
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Correspondence to Alberto S. Cattaneo.

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Cattaneo, A.S., Dherin, B. & Weinstein, A. Symplectic microgeometry II: generating functions. Bull Braz Math Soc, New Series 42, 507–536 (2011). https://doi.org/10.1007/s00574-011-0027-2

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  • DOI: https://doi.org/10.1007/s00574-011-0027-2

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