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
Instituto de Astrofísica de La Plata
Materia
Ciencias Astronómicas
Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
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:10915/93656

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network_name_str SEDICI (UNLP)
spelling Partially chaotic orbits in a perturbed cubic force modelMuzzio, Juan CarlosCiencias AstronómicasChaosNumerical methodsCelestial mechanicsKinematics (galaxias)Dynamics (galaxias)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 orbitInstituto de Astrofísica de La Plata2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf4099-4110http://sedici.unlp.edu.ar/handle/10915/93656enginfo: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/issn/0035-8711info:eu-repo/semantics/altIdentifier/doi/10.1093/mnras/stx1922info:eu-repo/semantics/altIdentifier/hdl/11336/35738info: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:UNLP2025-09-29T11:19:26Zoai:sedici.unlp.edu.ar:10915/93656Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:19:26.929SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Ciencias Astronómicas
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 Ciencias Astronómicas
Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
topic Ciencias Astronómicas
Chaos
Numerical methods
Celestial mechanics
Kinematics (galaxias)
Dynamics (galaxias)
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
Instituto de Astrofísica de La Plata
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
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/10915/93656
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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/issn/0035-8711
info:eu-repo/semantics/altIdentifier/doi/10.1093/mnras/stx1922
info:eu-repo/semantics/altIdentifier/hdl/11336/35738
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
4099-4110
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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