A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems

We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires that the Hamiltonian system has as many parameters as the dimension of the...

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Detalles Bibliográficos
Autores: Caracciolo, C., Figueras, J. L., Haro, A.
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/484463
Acceso en línea:http://hdl.handle.net/2072/484463
Access Level:acceso abierto
Palabra clave:KAM theory
Lower dimensional invariant tori
Parametrization method
51
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spelling A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systemsCaracciolo, C.Figueras, J. L.Haro, A.KAM theoryLower dimensional invariant toriParametrization method51We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires that the Hamiltonian system has as many parameters as the dimension of the normal dynamics, and the algorithm must adjust these parameters. We illustrate the methodology with an implementation of the algorithm computing 2-dimensional elliptic tori in a system of 4 coupled anharmonic oscillators (4 degrees of freedom).C C acknowledges the partial support from the scholarship \u2018Esseen, L. and C-G., for mathematical studies\u2019. J-L F has been partially supported by the Swedish VR Grant 2019-04591, and A H has been supported by the Spanish grant PID2021-125535NB-I00 (MCIU/AEI/FEDER, UE), and by the Spanish State Research Agency, through the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). Some computations were enabled by resources in project NAISS 2023/5-192 provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at UPPMAX, funded by the Swedish Research Council through Grant Agreement No. 2022-06725.info:eu-repo/semantics/publishedVersionInstitute of Physics2025info:eu-repo/semantics/article26 p.application/pdfhttp://hdl.handle.net/2072/484463RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésNonlinearityAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/4844632026-05-29T05:05:01Z
dc.title.none.fl_str_mv A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
title A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
spellingShingle A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
Caracciolo, C.
KAM theory
Lower dimensional invariant tori
Parametrization method
51
title_short A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
title_full A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
title_fullStr A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
title_full_unstemmed A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
title_sort A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
dc.creator.none.fl_str_mv Caracciolo, C.
Figueras, J. L.
Haro, A.
author Caracciolo, C.
author_facet Caracciolo, C.
Figueras, J. L.
Haro, A.
author_role author
author2 Figueras, J. L.
Haro, A.
author2_role author
author
dc.subject.none.fl_str_mv KAM theory
Lower dimensional invariant tori
Parametrization method
51
topic KAM theory
Lower dimensional invariant tori
Parametrization method
51
description We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires that the Hamiltonian system has as many parameters as the dimension of the normal dynamics, and the algorithm must adjust these parameters. We illustrate the methodology with an implementation of the algorithm computing 2-dimensional elliptic tori in a system of 4 coupled anharmonic oscillators (4 degrees of freedom).
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/484463
url http://hdl.handle.net/2072/484463
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinearity
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 26 p.
application/pdf
dc.publisher.none.fl_str_mv Institute of Physics
publisher.none.fl_str_mv Institute of Physics
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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