Flow map parameterization methods for invariant tori in Hamiltonian systems

The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), param...

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Detalles Bibliográficos
Autores: Haro, Àlex, Mondelo González, José María
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
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:2445/192644
Acceso en línea:https://hdl.handle.net/2445/192644
Access Level:acceso abierto
Palabra clave:Sistemes hamiltonians
Pertorbació (Matemàtica)
Equacions diferencials ordinàries
Hamiltonian systems
Perturbation (Mathematics)
Ordinary differential equations
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spelling Flow map parameterization methods for invariant tori in Hamiltonian systemsHaro, ÀlexMondelo González, José MaríaSistemes hamiltoniansPertorbació (Matemàtica)Equacions diferencials ordinàriesHamiltonian systemsPerturbation (Mathematics)Ordinary differential equationsThe goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), parameterization methods reduce the cost of a single step of the derived Newton-like method to be proportional to the cost of a FFT. Symplectic properties lead to some magic cancellations that make the methods work. The multiple shooting version of the methods are applied to the computation of invariant tori and their invariant bundles around librational equilibrium points of the Restricted Three Body Problem. The invariant bundles are the first order approximations of the corresponding invariant manifolds, commonly known as the whiskers, which are very important in the dynamical organization and have important applications in space mission design.Elsevier B.V.2023202320212023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/192644Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105859Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 101https://doi.org/10.1016/j.cnsns.2021.105859cc-by-nc-nd (c) Elsevier B.V., 2021https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1926442026-05-29T05:05:01Z
dc.title.none.fl_str_mv Flow map parameterization methods for invariant tori in Hamiltonian systems
title Flow map parameterization methods for invariant tori in Hamiltonian systems
spellingShingle Flow map parameterization methods for invariant tori in Hamiltonian systems
Haro, Àlex
Sistemes hamiltonians
Pertorbació (Matemàtica)
Equacions diferencials ordinàries
Hamiltonian systems
Perturbation (Mathematics)
Ordinary differential equations
title_short Flow map parameterization methods for invariant tori in Hamiltonian systems
title_full Flow map parameterization methods for invariant tori in Hamiltonian systems
title_fullStr Flow map parameterization methods for invariant tori in Hamiltonian systems
title_full_unstemmed Flow map parameterization methods for invariant tori in Hamiltonian systems
title_sort Flow map parameterization methods for invariant tori in Hamiltonian systems
dc.creator.none.fl_str_mv Haro, Àlex
Mondelo González, José María
author Haro, Àlex
author_facet Haro, Àlex
Mondelo González, José María
author_role author
author2 Mondelo González, José María
author2_role author
dc.subject.none.fl_str_mv Sistemes hamiltonians
Pertorbació (Matemàtica)
Equacions diferencials ordinàries
Hamiltonian systems
Perturbation (Mathematics)
Ordinary differential equations
topic Sistemes hamiltonians
Pertorbació (Matemàtica)
Equacions diferencials ordinàries
Hamiltonian systems
Perturbation (Mathematics)
Ordinary differential equations
description The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), parameterization methods reduce the cost of a single step of the derived Newton-like method to be proportional to the cost of a FFT. Symplectic properties lead to some magic cancellations that make the methods work. The multiple shooting version of the methods are applied to the computation of invariant tori and their invariant bundles around librational equilibrium points of the Restricted Three Body Problem. The invariant bundles are the first order approximations of the corresponding invariant manifolds, commonly known as the whiskers, which are very important in the dynamical organization and have important applications in space mission design.
publishDate 2021
dc.date.none.fl_str_mv 2021
2023
2023
2023
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/2445/192644
url https://hdl.handle.net/2445/192644
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105859
Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 101
https://doi.org/10.1016/j.cnsns.2021.105859
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier B.V., 2021
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier B.V., 2021
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
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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