Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem

We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors f...

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Autores: Llave, Ramon de la, Celletti, Alessandra, Gimeno i Alquézar, Joan, Calleja, Renato
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
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:2445/220218
Acceso en línea:https://hdl.handle.net/2445/220218
Access Level:acceso abierto
Palabra clave:Mecànica celeste
Sistemes dinàmics diferenciables
Celestial mechanics
Differentiable dynamical systems
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spelling Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problemLlave, Ramon de laCelletti, AlessandraGimeno i Alquézar, JoanCalleja, RenatoMecànica celesteSistemes dinàmics diferenciablesCelestial mechanicsDifferentiable dynamical systemsWe consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces.Springer Verlag2025202520232025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion38 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/220218Articles 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)InglésReproducció del document publicat a: https://doi.org/10.1007/s00332-023-09988-wJournal of Nonlinear Science, 2023, vol. 34https://doi.org/10.1007/s00332-023-09988-wcc by (c) Primer Renato Calleja et al., 2023http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2202182026-05-29T05:05:01Z
dc.title.none.fl_str_mv Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
title Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
spellingShingle Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
Llave, Ramon de la
Mecànica celeste
Sistemes dinàmics diferenciables
Celestial mechanics
Differentiable dynamical systems
title_short Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
title_full Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
title_fullStr Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
title_full_unstemmed Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
title_sort Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
dc.creator.none.fl_str_mv Llave, Ramon de la
Celletti, Alessandra
Gimeno i Alquézar, Joan
Calleja, Renato
author Llave, Ramon de la
author_facet Llave, Ramon de la
Celletti, Alessandra
Gimeno i Alquézar, Joan
Calleja, Renato
author_role author
author2 Celletti, Alessandra
Gimeno i Alquézar, Joan
Calleja, Renato
author2_role author
author
author
dc.subject.none.fl_str_mv Mecànica celeste
Sistemes dinàmics diferenciables
Celestial mechanics
Differentiable dynamical systems
topic Mecànica celeste
Sistemes dinàmics diferenciables
Celestial mechanics
Differentiable dynamical systems
description We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces.
publishDate 2023
dc.date.none.fl_str_mv 2023
2025
2025
2025
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 https://hdl.handle.net/2445/220218
url https://hdl.handle.net/2445/220218
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1007/s00332-023-09988-w
Journal of Nonlinear Science, 2023, vol. 34
https://doi.org/10.1007/s00332-023-09988-w
dc.rights.none.fl_str_mv cc by (c) Primer Renato Calleja et al., 2023
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) Primer Renato Calleja et al., 2023
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 38 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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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