Arnold diffusion: an overview through dynamical astronomy
- Autores
- Cincotta, Pablo Miguel
- Año de publicación
- 2002
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included.
Fil: Cincotta, Pablo Miguel. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. 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
-
Chaos
Diffusion
Instabilities
Galaxies
Dynamics (Galaxias) - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/36957
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Arnold diffusion: an overview through dynamical astronomyCincotta, Pablo MiguelChaosDiffusionInstabilitiesGalaxiesDynamics (Galaxias)https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included.Fil: Cincotta, Pablo Miguel. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. 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; ArgentinaElsevier2002-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/36957Cincotta, Pablo Miguel; Arnold diffusion: an overview through dynamical astronomy; Elsevier; New Astronomy Reviews; 46; 1; 12-2002; 13-391387-6473CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/S1387-6473(01)00153-1info:eu-repo/semantics/altIdentifier/url/http://adsabs.harvard.edu/abs/2002NewAR..46...13Cinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:30:54Zoai:ri.conicet.gov.ar:11336/36957instacron: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 10:30:54.4CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Arnold diffusion: an overview through dynamical astronomy |
title |
Arnold diffusion: an overview through dynamical astronomy |
spellingShingle |
Arnold diffusion: an overview through dynamical astronomy Cincotta, Pablo Miguel Chaos Diffusion Instabilities Galaxies Dynamics (Galaxias) |
title_short |
Arnold diffusion: an overview through dynamical astronomy |
title_full |
Arnold diffusion: an overview through dynamical astronomy |
title_fullStr |
Arnold diffusion: an overview through dynamical astronomy |
title_full_unstemmed |
Arnold diffusion: an overview through dynamical astronomy |
title_sort |
Arnold diffusion: an overview through dynamical astronomy |
dc.creator.none.fl_str_mv |
Cincotta, Pablo Miguel |
author |
Cincotta, Pablo Miguel |
author_facet |
Cincotta, Pablo Miguel |
author_role |
author |
dc.subject.none.fl_str_mv |
Chaos Diffusion Instabilities Galaxies Dynamics (Galaxias) |
topic |
Chaos Diffusion Instabilities Galaxies 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 |
The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included. Fil: Cincotta, Pablo Miguel. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. 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 |
The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-12 |
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/11336/36957 Cincotta, Pablo Miguel; Arnold diffusion: an overview through dynamical astronomy; Elsevier; New Astronomy Reviews; 46; 1; 12-2002; 13-39 1387-6473 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/36957 |
identifier_str_mv |
Cincotta, Pablo Miguel; Arnold diffusion: an overview through dynamical astronomy; Elsevier; New Astronomy Reviews; 46; 1; 12-2002; 13-39 1387-6473 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/S1387-6473(01)00153-1 info:eu-repo/semantics/altIdentifier/url/http://adsabs.harvard.edu/abs/2002NewAR..46...13C |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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