Finding how many isolating integrals of motion an orbit obeys

Autores
Carpintero, Daniel Diego
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The correlation dimension, that is the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of non-linear dynamics in order to compute the dimension of the manifold in which an orbit moves, without the need of knowing the actual equations of motion that give rise to the trajectory. This technique has been proposed in the past as a method to measure the dimension of stellar orbits in astronomical potentials, that is the number of isolating integrals of motion the orbits obey. Although the algorithm can in principle yield that number, some care has to be taken in order to obtain good results. We studied the relevant parameters of the technique, found their optimal values, and tested the validity of the method on a number of potentials previously studied in the literature, using the Smaller Alignment Index (SALI), Lyapunov exponents and spectral dynamics as gauges.
Instituto de Astrofísica de La Plata
Materia
Ciencias Astronómicas
Galaxies: kinematics and dynamics
Methods: numerical
Stellar dynamics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/84104
Acceder
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network_name_str SEDICI (UNLP)
spelling Finding how many isolating integrals of motion an orbit obeysCarpintero, Daniel DiegoCiencias AstronómicasGalaxies: kinematics and dynamicsMethods: numericalStellar dynamicsThe correlation dimension, that is the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of non-linear dynamics in order to compute the dimension of the manifold in which an orbit moves, without the need of knowing the actual equations of motion that give rise to the trajectory. This technique has been proposed in the past as a method to measure the dimension of stellar orbits in astronomical potentials, that is the number of isolating integrals of motion the orbits obey. Although the algorithm can in principle yield that number, some care has to be taken in order to obtain good results. We studied the relevant parameters of the technique, found their optimal values, and tested the validity of the method on a number of potentials previously studied in the literature, using the Smaller Alignment Index (SALI), Lyapunov exponents and spectral dynamics as gauges.Instituto de Astrofísica de La Plata2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1293-1304http://sedici.unlp.edu.ar/handle/10915/84104enginfo:eu-repo/semantics/altIdentifier/issn/0035-8711info:eu-repo/semantics/altIdentifier/doi/10.1111/j.1365-2966.2008.13469.xinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:16:11Zoai:sedici.unlp.edu.ar:10915/84104Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:16:11.436SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Finding how many isolating integrals of motion an orbit obeys
title Finding how many isolating integrals of motion an orbit obeys
spellingShingle Finding how many isolating integrals of motion an orbit obeys
Carpintero, Daniel Diego
Ciencias Astronómicas
Galaxies: kinematics and dynamics
Methods: numerical
Stellar dynamics
title_short Finding how many isolating integrals of motion an orbit obeys
title_full Finding how many isolating integrals of motion an orbit obeys
title_fullStr Finding how many isolating integrals of motion an orbit obeys
title_full_unstemmed Finding how many isolating integrals of motion an orbit obeys
title_sort Finding how many isolating integrals of motion an orbit obeys
dc.creator.none.fl_str_mv Carpintero, Daniel Diego
author Carpintero, Daniel Diego
author_facet Carpintero, Daniel Diego
author_role author
dc.subject.none.fl_str_mv Ciencias Astronómicas
Galaxies: kinematics and dynamics
Methods: numerical
Stellar dynamics
topic Ciencias Astronómicas
Galaxies: kinematics and dynamics
Methods: numerical
Stellar dynamics
dc.description.none.fl_txt_mv The correlation dimension, that is the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of non-linear dynamics in order to compute the dimension of the manifold in which an orbit moves, without the need of knowing the actual equations of motion that give rise to the trajectory. This technique has been proposed in the past as a method to measure the dimension of stellar orbits in astronomical potentials, that is the number of isolating integrals of motion the orbits obey. Although the algorithm can in principle yield that number, some care has to be taken in order to obtain good results. We studied the relevant parameters of the technique, found their optimal values, and tested the validity of the method on a number of potentials previously studied in the literature, using the Smaller Alignment Index (SALI), Lyapunov exponents and spectral dynamics as gauges.
Instituto de Astrofísica de La Plata
description The correlation dimension, that is the dimension obtained by computing the correlation function of pairs of points of a trajectory in phase space, is a numerical technique introduced in the field of non-linear dynamics in order to compute the dimension of the manifold in which an orbit moves, without the need of knowing the actual equations of motion that give rise to the trajectory. This technique has been proposed in the past as a method to measure the dimension of stellar orbits in astronomical potentials, that is the number of isolating integrals of motion the orbits obey. Although the algorithm can in principle yield that number, some care has to be taken in order to obtain good results. We studied the relevant parameters of the technique, found their optimal values, and tested the validity of the method on a number of potentials previously studied in the literature, using the Smaller Alignment Index (SALI), Lyapunov exponents and spectral dynamics as gauges.
publishDate 2008
dc.date.none.fl_str_mv 2008
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/84104
url http://sedici.unlp.edu.ar/handle/10915/84104
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0035-8711
info:eu-repo/semantics/altIdentifier/doi/10.1111/j.1365-2966.2008.13469.x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1293-1304
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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