Header

UZH-Logo

Maintenance Infos

Symplectic microgeometry II: generating functions


Cattaneo, A S; Dherin, B; Weinstein, A (2011). Symplectic microgeometry II: generating functions. Bulletin of the Brazilian Mathematical Society, N.S., 42(4):507-536.

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.

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.

Statistics

Citations

Dimensions.ai Metrics
9 citations in Web of Science®
9 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

145 downloads since deposited on 08 Jan 2012
20 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:2011
Deposited On:08 Jan 2012 19:28
Last Modified:23 Jan 2022 19:32
Publisher:Springer
ISSN:1678-7544
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00574-011-0027-2
Related URLs:http://arxiv.org/abs/1103.0672
  • Content: Accepted Version
  • Description: Version 1
  • Content: Accepted Version
  • Description: Version 2
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005