A differential equations approach to Hamiltonian systems
type: Item
instance of: scholarly article
title: A differential equations approach to Hamiltonian systems
zbMATH Open document ID: 1018.37035
DOI: 10.1016/S0034-4877(02)80032-5
author: Dirk Fesser
author: Dirk Saller
author: Werner M. Seiler
published in: Reports on Mathematical Physics
publication date: 2003-01-22T00:00:00Z
review text: The authors explore the geometric model for time-dependent Hamiltonian systems which starts from a cosymplectic manifold \(M\). Constraints correspond to a given submanifold \(N\subset M\) and have to be handled in such a model via a Gotay-Nester type algorithm. Assuming \(M\) is fibred over a one-dimensional base and the Reeb vector field is transversal to the fibration, Hamiltonian differential equations are identified with a fibred submanifold of the first-jet bundle \(J_1M\). The main result of the paper is the proof of equivalence of the aforementioned constraint algorithm with the completion algorithm for obtaining formally integrable differential equations in the sense of the Cartan-Kuranishi theorem. As a kind of application, some aspects of a covariant formulation of classical mechanics are discussed. The paper ends with a brief outline of the difficulties one has to address for a generalization to field theories.
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 70H45
zbMATH DE Number: 1857369
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: cosymplectic manifold
zbMATH Keywords: formal integrability
zbMATH Keywords: constraint algorithm
reviewed by: W. Sarlet
MaRDI profile type: Publication
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full work available at URL: s0034-4877(02)80032-5
OpenAlex ID: W1983545450
description: scientific article; zbMATH DE number 1857369