Singular reduction of resonant Hamiltonians

This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://...

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Autores: Meyer, Kenneth Ray, Palacián Subiela, Jesús Francisco, Yanguas Sayas, Patricia
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/28577
Acceso en línea:https://hdl.handle.net/2454/28577
Access Level:acceso abierto
Palabra clave:Normal form and resonant Hamiltonian
Singular reduction
Cross section
Orbit space and orbifold
Plateau
Peak and ridge
Symplectic coordinates and symplectic smoothing
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spelling Singular reduction of resonant HamiltoniansMeyer, Kenneth RayPalacián Subiela, Jesús FranciscoYanguas Sayas, PatriciaNormal form and resonant HamiltonianSingular reductionCross sectionOrbit space and orbifoldPlateauPeak and ridgeSymplectic coordinates and symplectic smoothingThis is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aab591.We investigate the dynamics of resonant Hamiltonians with n degrees of freedom to which we attach a small perturbation. Our study is based on the geometric interpretation of singular reduction theory. The flow of the Hamiltonian vector field is reconstructed from the cross sections corresponding to an approximation of this vector field in an energy surface. This approximate system is also built using normal forms and applying reduction theory obtaining the reduced Hamiltonian that is defined on the orbit space. Generically, the reduction is of singular character and we classify the singularities in the orbit space, getting three different types of singular points. A critical point of the reduced Hamiltonian corresponds to a family of periodic solutions in the full system whose characteristic multipliers are approximated accordingly to the nature of the critical point.The authors are partially supported by Projects MTM 2011-28227-C02-01 of the Ministry of Science and Innovation of Spain, MTM 2014-59433-C2-1-P of the Ministry of Economy and Competitiveness of Spain and by the Charles Phelps Taft Foundation.IOP PublishingLondon Mathematical SocietyMatematika eta Informatika IngeniaritzaInstitute for Advanced Materials and Mathematics - INAMAT2Ingeniería Matemática e Informática2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/28577reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P© 2018 IOP Publishing Ltd & London Mathematical Societyinfo:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/285772026-06-17T12:41:47Z
dc.title.none.fl_str_mv Singular reduction of resonant Hamiltonians
title Singular reduction of resonant Hamiltonians
spellingShingle Singular reduction of resonant Hamiltonians
Meyer, Kenneth Ray
Normal form and resonant Hamiltonian
Singular reduction
Cross section
Orbit space and orbifold
Plateau
Peak and ridge
Symplectic coordinates and symplectic smoothing
title_short Singular reduction of resonant Hamiltonians
title_full Singular reduction of resonant Hamiltonians
title_fullStr Singular reduction of resonant Hamiltonians
title_full_unstemmed Singular reduction of resonant Hamiltonians
title_sort Singular reduction of resonant Hamiltonians
dc.creator.none.fl_str_mv Meyer, Kenneth Ray
Palacián Subiela, Jesús Francisco
Yanguas Sayas, Patricia
author Meyer, Kenneth Ray
author_facet Meyer, Kenneth Ray
Palacián Subiela, Jesús Francisco
Yanguas Sayas, Patricia
author_role author
author2 Palacián Subiela, Jesús Francisco
Yanguas Sayas, Patricia
author2_role author
author
dc.contributor.none.fl_str_mv Matematika eta Informatika Ingeniaritza
Institute for Advanced Materials and Mathematics - INAMAT2
Ingeniería Matemática e Informática
dc.subject.none.fl_str_mv Normal form and resonant Hamiltonian
Singular reduction
Cross section
Orbit space and orbifold
Plateau
Peak and ridge
Symplectic coordinates and symplectic smoothing
topic Normal form and resonant Hamiltonian
Singular reduction
Cross section
Orbit space and orbifold
Plateau
Peak and ridge
Symplectic coordinates and symplectic smoothing
description This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aab591.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/28577
url https://hdl.handle.net/2454/28577
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01
info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P
dc.rights.none.fl_str_mv © 2018 IOP Publishing Ltd & London Mathematical Society
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2018 IOP Publishing Ltd & London Mathematical Society
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
London Mathematical Society
publisher.none.fl_str_mv IOP Publishing
London Mathematical Society
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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