The Hamiltonian tube of a cotangent-lifted action

The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in normal form the existing symplectic structure and momentum map. The main drawb...

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Autores: Rodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111, Teixidó Román, Miguel|||0000-0002-7090-7228
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/108284
Acceso en línea:https://hdl.handle.net/2117/108284
https://dx.doi.org/10.4310/JSG.2017.v15.n3.a7
Access Level:acceso abierto
Palabra clave:Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
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spelling The Hamiltonian tube of a cotangent-lifted actionRodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111Teixidó Román, Miguel|||0000-0002-7090-7228Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometryÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencialThe Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in normal form the existing symplectic structure and momentum map. The main drawback of the MGS form is that it does not have an explicit expression. We will obtain a MGS form for cotangent-lifted actions on cotangent bundles that, in addition to its defining features, respects the additional fibered structure present. This model generalizes previous results obtained by T. Schmah for orbits with fully-isotropic momentum. In addition, our construction is explicit up to the integration of a differential equation on G. This equation can be easily solved for the groups SO(3) or SL(2), thus giving explicit symplectic coordinates for arbitrary canonical actions of these groups on any cotangent bundle.Peer Reviewed20172017-01-0120172017-10-02journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/108284https://dx.doi.org/10.4310/JSG.2017.v15.n3.a7reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1082842026-05-27T15:37:01Z
dc.title.none.fl_str_mv The Hamiltonian tube of a cotangent-lifted action
title The Hamiltonian tube of a cotangent-lifted action
spellingShingle The Hamiltonian tube of a cotangent-lifted action
Rodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
title_short The Hamiltonian tube of a cotangent-lifted action
title_full The Hamiltonian tube of a cotangent-lifted action
title_fullStr The Hamiltonian tube of a cotangent-lifted action
title_full_unstemmed The Hamiltonian tube of a cotangent-lifted action
title_sort The Hamiltonian tube of a cotangent-lifted action
dc.creator.none.fl_str_mv Rodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111
Teixidó Román, Miguel|||0000-0002-7090-7228
author Rodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111
author_facet Rodríguez Olmos, Miguel Andrés|||0000-0003-2378-4111
Teixidó Román, Miguel|||0000-0002-7090-7228
author_role author
author2 Teixidó Román, Miguel|||0000-0002-7090-7228
author2_role author
dc.subject.none.fl_str_mv Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
topic Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
description The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in normal form the existing symplectic structure and momentum map. The main drawback of the MGS form is that it does not have an explicit expression. We will obtain a MGS form for cotangent-lifted actions on cotangent bundles that, in addition to its defining features, respects the additional fibered structure present. This model generalizes previous results obtained by T. Schmah for orbits with fully-isotropic momentum. In addition, our construction is explicit up to the integration of a differential equation on G. This equation can be easily solved for the groups SO(3) or SL(2), thus giving explicit symplectic coordinates for arbitrary canonical actions of these groups on any cotangent bundle.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
2017
2017-10-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/108284
https://dx.doi.org/10.4310/JSG.2017.v15.n3.a7
url https://hdl.handle.net/2117/108284
https://dx.doi.org/10.4310/JSG.2017.v15.n3.a7
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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