Analysis of round off errors with reversibility test as a dynamical indicator

Autores
Faranda, Davide; Mestre, Martin Federico; Turchetti, Giorgio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analyzed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps, the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps, the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described.
Fil: Faranda, Davide. Universidad de Bologna; Italia
Fil: Mestre, Martin Federico. 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: Turchetti, Giorgio. Universidad de Bologna; Italia
Materia
Discrete Time Dynamical Systems
Gali
Lce
Megno
Mlce
Reversibility Error
Sali
Standard Map
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:11336/82526
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/82526
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Analysis of round off errors with reversibility test as a dynamical indicatorFaranda, DavideMestre, Martin FedericoTurchetti, GiorgioDiscrete Time Dynamical SystemsGaliLceMegnoMlceReversibility ErrorSaliStandard Maphttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analyzed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps, the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps, the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described.Fil: Faranda, Davide. Universidad de Bologna; ItaliaFil: Mestre, Martin Federico. 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: Turchetti, Giorgio. Universidad de Bologna; ItaliaWorld Scientific2012-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/82526Faranda, Davide; Mestre, Martin Federico; Turchetti, Giorgio; Analysis of round off errors with reversibility test as a dynamical indicator; World Scientific; International Journal Of Bifurcation And Chaos; 22; 9; 9-2012; 1250215-12502290218-1274CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S021812741250215Xinfo:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/pdf/10.1142/S021812741250215Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:11:03Zoai:ri.conicet.gov.ar:11336/82526instacron: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 10:11:04.055CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Analysis of round off errors with reversibility test as a dynamical indicator
title Analysis of round off errors with reversibility test as a dynamical indicator
spellingShingle Analysis of round off errors with reversibility test as a dynamical indicator
Faranda, Davide
Discrete Time Dynamical Systems
Gali
Lce
Megno
Mlce
Reversibility Error
Sali
Standard Map
title_short Analysis of round off errors with reversibility test as a dynamical indicator
title_full Analysis of round off errors with reversibility test as a dynamical indicator
title_fullStr Analysis of round off errors with reversibility test as a dynamical indicator
title_full_unstemmed Analysis of round off errors with reversibility test as a dynamical indicator
title_sort Analysis of round off errors with reversibility test as a dynamical indicator
dc.creator.none.fl_str_mv Faranda, Davide
Mestre, Martin Federico
Turchetti, Giorgio
author Faranda, Davide
author_facet Faranda, Davide
Mestre, Martin Federico
Turchetti, Giorgio
author_role author
author2 Mestre, Martin Federico
Turchetti, Giorgio
author2_role author
author
dc.subject.none.fl_str_mv Discrete Time Dynamical Systems
Gali
Lce
Megno
Mlce
Reversibility Error
Sali
Standard Map
topic Discrete Time Dynamical Systems
Gali
Lce
Megno
Mlce
Reversibility Error
Sali
Standard Map
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analyzed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps, the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps, the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described.
Fil: Faranda, Davide. Universidad de Bologna; Italia
Fil: Mestre, Martin Federico. 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: Turchetti, Giorgio. Universidad de Bologna; Italia
description We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analyzed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps, the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps, the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described.
publishDate 2012
dc.date.none.fl_str_mv 2012-09
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/11336/82526
Faranda, Davide; Mestre, Martin Federico; Turchetti, Giorgio; Analysis of round off errors with reversibility test as a dynamical indicator; World Scientific; International Journal Of Bifurcation And Chaos; 22; 9; 9-2012; 1250215-1250229
0218-1274
CONICET Digital
CONICET
url http://hdl.handle.net/11336/82526
identifier_str_mv Faranda, Davide; Mestre, Martin Federico; Turchetti, Giorgio; Analysis of round off errors with reversibility test as a dynamical indicator; World Scientific; International Journal Of Bifurcation And Chaos; 22; 9; 9-2012; 1250215-1250229
0218-1274
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S021812741250215X
info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/pdf/10.1142/S021812741250215X
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 World Scientific
publisher.none.fl_str_mv World Scientific
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 13.070432

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