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.

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.

Citations

4 citations in Web of Science®
4 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

75 downloads since deposited on 08 Jan 2012
13 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
Language:English
Date:2011
Deposited On:08 Jan 2012 19:28
Last Modified:05 Apr 2016 15:06
Publisher:Springer
ISSN:1678-7544
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00574-011-0027-2
Related URLs:http://arxiv.org/abs/1103.0672
Permanent URL: https://doi.org/10.5167/uzh-50967

Download

[img]
Content: Published Version
Language: English
Filetype: PDF - Registered users only
Size: 254kB
View at publisher
[img]
Preview
Content: Accepted Version
Filetype: PDF (Version 1)
Size: 304kB
[img]
Preview
Content: Accepted Version
Filetype: PDF (Version 2)
Size: 315kB

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations