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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/93656
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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 |
url |
http://sedici.unlp.edu.ar/handle/10915/93656 |
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 |
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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) |
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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 |
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SEDICI (UNLP) - Universidad Nacional de La Plata |
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