Hamiltonian structures for projectable dynamics on symplectic fiber bundles
type: Item
instance of: scholarly article
title: Hamiltonian structures for projectable dynamics on symplectic fiber bundles
zbMATH Open document ID: 1263.53075
author: Guillermo Dávila-Rascón
author: Yuri M. Vorobiev
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-19T00:00:00Z
review text: This work is a study of the Hamiltonization problem for projectable dynamics on general symplectic bundles. Let us recall that linearized dynamics does not inherit any natural Hamiltonian structure in general. The Hamiltonization problem for linearized dynamics has been extensively developed. In this paper, the purpose is to study this problem in a general setting. The author obtains necessary and sufficient conditions for the existence of Hamiltonian structures in terms of invariant symplectic connections. When the symplectic bundle is flat, it is proved that the conditions lead to study the solvability of linear differential equations of the homological type. Some versions of the conditions in the cases of exact symplectic bundles and symplectic vector bundles are also discussed.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 70H09
zbMATH DE Number: 6155708
zbMATH Keywords: Hamiltonization problem
zbMATH Keywords: symplectic fiber bundles
zbMATH Keywords: projectable systems
zbMATH Keywords: invariant symplectic connections
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.1077
OpenAlex ID: W2321207361
DOI: 10.3934/DCDS.2013.33.1077
description: scientific article; zbMATH DE number 6155708