Symplectic microgeometry II: generating functions

Autor(es)

Cattaneo, Alberto S. ^[1] ; Dherin, Benoit ^[2] ; Weinstein, Alan ^[3]

Afiliação do(s) autor(es)

^[1] Univ Zurich, Inst Math, CH-8057 Zurich - Switzerland

^[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 - USA

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 42, n. 4, p. 507-536, DEC 2011.
• Citações Web of Science: 8

Resumo

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. (AU)

• Processo FAPESP: 10/15069-8 - Geometrias monoidais
• Beneficiário: Benoit Richard Umbert Dherin
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores