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.
Fil: Carpintero, Daniel Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
Materia
GALAXIES: KINEMATICS AND DYNAMICS
METHODS: NUMERICAL
STELLAR DYNAMICS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/82483
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Finding how many isolating integrals of motion an orbit obeysCarpintero, Daniel DiegoGALAXIES: KINEMATICS AND DYNAMICSMETHODS: NUMERICALSTELLAR DYNAMICShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The 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.Fil: Carpintero, Daniel Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaOxford University Press2008-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/82483Carpintero, Daniel Diego; Finding how many isolating integrals of motion an orbit obeys; Oxford University Press; Monthly Notices of the Royal Astronomical Society; 388; 3; 8-2008; 1293-13040035-8711CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1111/j.1365-2966.2008.13469.xinfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/mnras/article/388/3/1293/956321info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:00:47Zoai:ri.conicet.gov.ar:11336/82483instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:00:47.864CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
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 GALAXIES: KINEMATICS AND DYNAMICS
METHODS: NUMERICAL
STELLAR DYNAMICS
topic GALAXIES: KINEMATICS AND DYNAMICS
METHODS: NUMERICAL
STELLAR DYNAMICS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
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.
Fil: Carpintero, Daniel Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
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 2008-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/82483
Carpintero, Daniel Diego; Finding how many isolating integrals of motion an orbit obeys; Oxford University Press; Monthly Notices of the Royal Astronomical Society; 388; 3; 8-2008; 1293-1304
0035-8711
CONICET Digital
CONICET
url http://hdl.handle.net/11336/82483
identifier_str_mv Carpintero, Daniel Diego; Finding how many isolating integrals of motion an orbit obeys; Oxford University Press; Monthly Notices of the Royal Astronomical Society; 388; 3; 8-2008; 1293-1304
0035-8711
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1111/j.1365-2966.2008.13469.x
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/mnras/article/388/3/1293/956321
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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