Chaos indicators and a spectral analysis: application to a self-consistent triaxial model

Autores
Maffione, Nicolas Pablo; Darriba, Luciano Ariel; Cincotta, Pablo Miguel; Giordano, Claudia Marcela
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Together with the variational indicators of chaos, the spectral analysis methods have also achieved great popularity in the field of chaos detection. The former are based on the concept of local exponential divergence. The latter are based on the numerical analysis of some particular quantities of a single orbit, e.g. its frequency. In spite of having totally different conceptual bases, they are used for the very same goals such as, for instance, separating the chaotic and the regular components. In fact, we show herein that the variational indicators serve to distinguish both components of a Hamiltonian system in a more reliable fashion than a spectral analysis method does. We study two start spaces for different energy levels of a self-consistent triaxial stellar dynamical model by means of some selected variational indicators and a spectral analysis method. In order to select the appropriate tools for this paper, we extend previous studies where we make a comparison of several variational indicators on different scenarios. Herein, we compare the average power-law exponent (APLE) and an alternative quantity given by the mean exponential growth factor of nearby orbits (MEGNO): the MEGNO's slope estimation of the largest Lyapunov characteristic exponent (SElLCE). The spectral analysis method selected for the investigation is the frequency modified Fourier transform (FMFT). Besides a comparative study of the APLE, the fast Lyapunov indicator (FLI), the orthogonal fast Lyapunov indicator (OFLI) and the MEGNO/SElLCE, we show that the SElLCE could be an appropriate alternative to the MEGNO when studying large samples of initial conditions. The SElLCE separates the chaotic and the regular components reliably and identifies the different levels of chaoticity. We show that the FMFT is not as reliable as the SElLCE to describe clearly the chaotic domains in the experiments. We use the latter indicator as the main variational indicator to analyse the phase space portraits of the model under study.
Fil: Maffione, Nicolas Pablo. 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
Fil: Darriba, Luciano Ariel. 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
Fil: Cincotta, Pablo Miguel. 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
Fil: Giordano, Claudia Marcela. 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
Numerical methods
Galaxies
Kinematics
Dynamics
Nivel de accesibilidad
acceso abierto
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
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CONICET Digital (CONICET)
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Consejo Nacional de Investigaciones Científicas y Técnicas
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spelling Chaos indicators and a spectral analysis: application to a self-consistent triaxial modelMaffione, Nicolas PabloDarriba, Luciano ArielCincotta, Pablo MiguelGiordano, Claudia MarcelaNumerical methodsGalaxiesKinematicsDynamicshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Together with the variational indicators of chaos, the spectral analysis methods have also achieved great popularity in the field of chaos detection. The former are based on the concept of local exponential divergence. The latter are based on the numerical analysis of some particular quantities of a single orbit, e.g. its frequency. In spite of having totally different conceptual bases, they are used for the very same goals such as, for instance, separating the chaotic and the regular components. In fact, we show herein that the variational indicators serve to distinguish both components of a Hamiltonian system in a more reliable fashion than a spectral analysis method does. We study two start spaces for different energy levels of a self-consistent triaxial stellar dynamical model by means of some selected variational indicators and a spectral analysis method. In order to select the appropriate tools for this paper, we extend previous studies where we make a comparison of several variational indicators on different scenarios. Herein, we compare the average power-law exponent (APLE) and an alternative quantity given by the mean exponential growth factor of nearby orbits (MEGNO): the MEGNO's slope estimation of the largest Lyapunov characteristic exponent (SElLCE). The spectral analysis method selected for the investigation is the frequency modified Fourier transform (FMFT). Besides a comparative study of the APLE, the fast Lyapunov indicator (FLI), the orthogonal fast Lyapunov indicator (OFLI) and the MEGNO/SElLCE, we show that the SElLCE could be an appropriate alternative to the MEGNO when studying large samples of initial conditions. The SElLCE separates the chaotic and the regular components reliably and identifies the different levels of chaoticity. We show that the FMFT is not as reliable as the SElLCE to describe clearly the chaotic domains in the experiments. We use the latter indicator as the main variational indicator to analyse the phase space portraits of the model under study.Fil: Maffione, Nicolas Pablo. 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; ArgentinaFil: Darriba, Luciano Ariel. 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; ArgentinaFil: Cincotta, Pablo Miguel. 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; ArgentinaFil: Giordano, Claudia Marcela. 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 Press2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19874Maffione, Nicolas Pablo; Darriba, Luciano Ariel; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Chaos indicators and a spectral analysis: application to a self-consistent triaxial model; Oxford University Press; Monthly Notices Of The Royal Astronomical Society; 429; 3; 3-2013; 2700-27170035-8711CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/mnras/sts539info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/sts539info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:44:46Zoai:ri.conicet.gov.ar:11336/19874instacron: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:34982025-09-29 09:44:46.773CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
title Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
spellingShingle Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
Maffione, Nicolas Pablo
Numerical methods
Galaxies
Kinematics
Dynamics
title_short Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
title_full Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
title_fullStr Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
title_full_unstemmed Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
title_sort Chaos indicators and a spectral analysis: application to a self-consistent triaxial model
dc.creator.none.fl_str_mv Maffione, Nicolas Pablo
Darriba, Luciano Ariel
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author Maffione, Nicolas Pablo
author_facet Maffione, Nicolas Pablo
Darriba, Luciano Ariel
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author_role author
author2 Darriba, Luciano Ariel
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author2_role author
author
author
dc.subject.none.fl_str_mv Numerical methods
Galaxies
Kinematics
Dynamics
topic Numerical methods
Galaxies
Kinematics
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 Together with the variational indicators of chaos, the spectral analysis methods have also achieved great popularity in the field of chaos detection. The former are based on the concept of local exponential divergence. The latter are based on the numerical analysis of some particular quantities of a single orbit, e.g. its frequency. In spite of having totally different conceptual bases, they are used for the very same goals such as, for instance, separating the chaotic and the regular components. In fact, we show herein that the variational indicators serve to distinguish both components of a Hamiltonian system in a more reliable fashion than a spectral analysis method does. We study two start spaces for different energy levels of a self-consistent triaxial stellar dynamical model by means of some selected variational indicators and a spectral analysis method. In order to select the appropriate tools for this paper, we extend previous studies where we make a comparison of several variational indicators on different scenarios. Herein, we compare the average power-law exponent (APLE) and an alternative quantity given by the mean exponential growth factor of nearby orbits (MEGNO): the MEGNO's slope estimation of the largest Lyapunov characteristic exponent (SElLCE). The spectral analysis method selected for the investigation is the frequency modified Fourier transform (FMFT). Besides a comparative study of the APLE, the fast Lyapunov indicator (FLI), the orthogonal fast Lyapunov indicator (OFLI) and the MEGNO/SElLCE, we show that the SElLCE could be an appropriate alternative to the MEGNO when studying large samples of initial conditions. The SElLCE separates the chaotic and the regular components reliably and identifies the different levels of chaoticity. We show that the FMFT is not as reliable as the SElLCE to describe clearly the chaotic domains in the experiments. We use the latter indicator as the main variational indicator to analyse the phase space portraits of the model under study.
Fil: Maffione, Nicolas Pablo. 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
Fil: Darriba, Luciano Ariel. 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
Fil: Cincotta, Pablo Miguel. 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
Fil: Giordano, Claudia Marcela. 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 Together with the variational indicators of chaos, the spectral analysis methods have also achieved great popularity in the field of chaos detection. The former are based on the concept of local exponential divergence. The latter are based on the numerical analysis of some particular quantities of a single orbit, e.g. its frequency. In spite of having totally different conceptual bases, they are used for the very same goals such as, for instance, separating the chaotic and the regular components. In fact, we show herein that the variational indicators serve to distinguish both components of a Hamiltonian system in a more reliable fashion than a spectral analysis method does. We study two start spaces for different energy levels of a self-consistent triaxial stellar dynamical model by means of some selected variational indicators and a spectral analysis method. In order to select the appropriate tools for this paper, we extend previous studies where we make a comparison of several variational indicators on different scenarios. Herein, we compare the average power-law exponent (APLE) and an alternative quantity given by the mean exponential growth factor of nearby orbits (MEGNO): the MEGNO's slope estimation of the largest Lyapunov characteristic exponent (SElLCE). The spectral analysis method selected for the investigation is the frequency modified Fourier transform (FMFT). Besides a comparative study of the APLE, the fast Lyapunov indicator (FLI), the orthogonal fast Lyapunov indicator (OFLI) and the MEGNO/SElLCE, we show that the SElLCE could be an appropriate alternative to the MEGNO when studying large samples of initial conditions. The SElLCE separates the chaotic and the regular components reliably and identifies the different levels of chaoticity. We show that the FMFT is not as reliable as the SElLCE to describe clearly the chaotic domains in the experiments. We use the latter indicator as the main variational indicator to analyse the phase space portraits of the model under study.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/19874
Maffione, Nicolas Pablo; Darriba, Luciano Ariel; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Chaos indicators and a spectral analysis: application to a self-consistent triaxial model; Oxford University Press; Monthly Notices Of The Royal Astronomical Society; 429; 3; 3-2013; 2700-2717
0035-8711
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19874
identifier_str_mv Maffione, Nicolas Pablo; Darriba, Luciano Ariel; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Chaos indicators and a spectral analysis: application to a self-consistent triaxial model; Oxford University Press; Monthly Notices Of The Royal Astronomical Society; 429; 3; 3-2013; 2700-2717
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/10.1093/mnras/sts539
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/sts539
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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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)
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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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