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Singular reduction of resonant Hamiltonians
dc.creator | Meyer, Kenneth Ray | es_ES |
dc.creator | Palacián Subiela, Jesús Francisco | es_ES |
dc.creator | Yanguas Sayas, Patricia | es_ES |
dc.date.accessioned | 2018-05-09T15:17:46Z | |
dc.date.available | 2019-05-08T23:00:13Z | |
dc.date.issued | 2018 | |
dc.identifier.issn | 0951-7715 (Print) | |
dc.identifier.issn | 1361-6544 (Electronic) | |
dc.identifier.uri | https://hdl.handle.net/2454/28577 | |
dc.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. | en |
dc.description.abstract | 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. | en |
dc.description.sponsorship | 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. | en |
dc.format.mimetype | application/pdf | en |
dc.language.iso | eng | en |
dc.publisher | IOP Publishing | en |
dc.publisher | London Mathematical Society | en |
dc.relation.ispartof | Nonlinearity, vol. 31, n. 6 | en |
dc.rights | © 2018 IOP Publishing Ltd & London Mathematical Society | en |
dc.subject | Normal form and resonant Hamiltonian | en |
dc.subject | Singular reduction | en |
dc.subject | Cross section | en |
dc.subject | Orbit space and orbifold | en |
dc.subject | Plateau | en |
dc.subject | Peak and ridge | en |
dc.subject | Symplectic coordinates and symplectic smoothing | en |
dc.title | Singular reduction of resonant Hamiltonians | en |
dc.type | Artículo / Artikulua | es |
dc.type | info:eu-repo/semantics/article | en |
dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | es_ES |
dc.rights.accessRights | Acceso abierto / Sarbide irekia | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
dc.embargo.terms | 2019-05-08 | |
dc.identifier.doi | 10.1088/1361-6544/aab591 | |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01/ES/ | en |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P/ES/ | en |
dc.relation.publisherversion | https://doi.org/10.1088/1361-6544/aab591 | |
dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
dc.type.version | info:eu-repo/semantics/acceptedVersion | en |