Partially chaotic orbits in a perturbed cubic force model

Autores
Muzzio, Juan Carlos
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincare maps to show that partially chaotic orbits ´ are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit
Fil: Muzzio, Juan Carlos. 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. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Materia
Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
Nivel de accesibilidad
acceso abierto
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
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Consejo Nacional de Investigaciones Científicas y Técnicas
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oai:ri.conicet.gov.ar:11336/35738
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network_name_str CONICET Digital (CONICET)
spelling Partially chaotic orbits in a perturbed cubic force modelMuzzio, Juan CarlosChaosNumerical methodsCelestial mechanicsKinematics (galaxias)Dynamics (galaxias)https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincare maps to show that partially chaotic orbits ´ are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbitFil: Muzzio, Juan Carlos. 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. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaWiley Blackwell Publishing, Inc2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/35738Muzzio, Juan Carlos; Partially chaotic orbits in a perturbed cubic force model; Wiley Blackwell Publishing, Inc; Monthly Notices of the Royal Astronomical Society; 471; 4; 11-2017; 4099-41100035-8711CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://academic.oup.com/mnras/article/471/4/4099/4044715/Partially-chaotic-orbits-in-a-perturbed-cubicinfo:eu-repo/semantics/altIdentifier/doi/10.1093/mnras/stx1922info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:57:32Zoai:ri.conicet.gov.ar:11336/35738instacron: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 11:57:33.179CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Partially chaotic orbits in a perturbed cubic force model
title Partially chaotic orbits in a perturbed cubic force model
spellingShingle Partially chaotic orbits in a perturbed cubic force model
Muzzio, Juan Carlos
Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
title_short Partially chaotic orbits in a perturbed cubic force model
title_full Partially chaotic orbits in a perturbed cubic force model
title_fullStr Partially chaotic orbits in a perturbed cubic force model
title_full_unstemmed Partially chaotic orbits in a perturbed cubic force model
title_sort Partially chaotic orbits in a perturbed cubic force model
dc.creator.none.fl_str_mv Muzzio, Juan Carlos
author Muzzio, Juan Carlos
author_facet Muzzio, Juan Carlos
author_role author
dc.subject.none.fl_str_mv Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
topic Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincare maps to show that partially chaotic orbits ´ are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit
Fil: Muzzio, Juan Carlos. 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. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
description Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincare maps to show that partially chaotic orbits ´ are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit
publishDate 2017
dc.date.none.fl_str_mv 2017-11
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/11336/35738
Muzzio, Juan Carlos; Partially chaotic orbits in a perturbed cubic force model; Wiley Blackwell Publishing, Inc; Monthly Notices of the Royal Astronomical Society; 471; 4; 11-2017; 4099-4110
0035-8711
CONICET Digital
CONICET
url http://hdl.handle.net/11336/35738
identifier_str_mv Muzzio, Juan Carlos; Partially chaotic orbits in a perturbed cubic force model; Wiley Blackwell Publishing, Inc; Monthly Notices of the Royal Astronomical Society; 471; 4; 11-2017; 4099-4110
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/url/http://academic.oup.com/mnras/article/471/4/4099/4044715/Partially-chaotic-orbits-in-a-perturbed-cubic
info:eu-repo/semantics/altIdentifier/doi/10.1093/mnras/stx1922
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 Wiley Blackwell Publishing, Inc
publisher.none.fl_str_mv Wiley Blackwell Publishing, Inc
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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