Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem

There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary finite dimension. The setting in which the dimension is larg...

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Detalles Bibliográficos
Autores: Baldomá, I., Fontich, E., Martín, P.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
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:2072/537716
Acceso en línea:http://hdl.handle.net/2072/537716
Access Level:acceso abierto
Palabra clave:Invariant Manifolds
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spelling Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body ProblemBaldomá, I.Fontich, E.Martín, P.Invariant ManifoldsThere are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary finite dimension. The setting in which the dimension is larger than one was not previously considered and is technically more involved because in such case the invariant manifolds do not have, in general, polynomial approximations. As an example, we apply our theorem to prove that there are motions in the (n +2)-body problem in which the distances among the first n bodies remain bounded for all time, while the relative distances between the first n-bodies and the last two and the distances between the last bodies tend to infinity, when time goes to infinity. Moreover, we prove that the final motion of the first n bodies corresponds to aKAM torus of the n-body problem.I.B. has been partially supported by the grant PID-2021-122954NB-100, E.F. has been partially supported by the grant PID2021-125535NB-I00, and P.M. has been partially supported by the grant PID2021-123968NB-I00, funded by the Spanish State Research Agency through the programs MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”.Also, all authors have been partially supported by the Spanish State Research Agency, through the Severo Ochoa andMaría de Maeztu Program for Centers andUnits of Excellence in R&D (CEX2020-001084-M).Springer2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion94 p.application/pdfhttp://hdl.handle.net/2072/537716RECERCAT (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)InglésArchive for Rational Mechanics and AnalysisL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5377162026-05-29T05:05:01Z
dc.title.none.fl_str_mv Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
title Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
spellingShingle Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
Baldomá, I.
Invariant Manifolds
title_short Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
title_full Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
title_fullStr Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
title_full_unstemmed Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
title_sort Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the (n + 2)-Body Problem
dc.creator.none.fl_str_mv Baldomá, I.
Fontich, E.
Martín, P.
author Baldomá, I.
author_facet Baldomá, I.
Fontich, E.
Martín, P.
author_role author
author2 Fontich, E.
Martín, P.
author2_role author
author
dc.subject.none.fl_str_mv Invariant Manifolds
topic Invariant Manifolds
description There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary finite dimension. The setting in which the dimension is larger than one was not previously considered and is technically more involved because in such case the invariant manifolds do not have, in general, polynomial approximations. As an example, we apply our theorem to prove that there are motions in the (n +2)-body problem in which the distances among the first n bodies remain bounded for all time, while the relative distances between the first n-bodies and the last two and the distances between the last bodies tend to infinity, when time goes to infinity. Moreover, we prove that the final motion of the first n bodies corresponds to aKAM torus of the n-body problem.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/537716
url http://hdl.handle.net/2072/537716
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Archive for Rational Mechanics and Analysis
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 94 p.
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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