Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures
- Autores
- Grillo, Sergio Daniel; Padrón, Edith
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper, we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi equation related to these systems. Then, we show that, for a given contact system, the knowledge of what we have called a complete pseudo-isotropic solution ensures the integrability by quadratures of its equations of motion. This extends to contact manifolds a recent result obtained in the context of general symplectic and Poisson manifolds.
Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Padrón, Edith. Universidad de La Laguna; España - Materia
-
Hamilton-Jacobi
Contact manifolds
Integrable systems - 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:11336/126256
Ver los metadatos del registro completo
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Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadraturesGrillo, Sergio DanielPadrón, EdithHamilton-JacobiContact manifoldsIntegrable systemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper, we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi equation related to these systems. Then, we show that, for a given contact system, the knowledge of what we have called a complete pseudo-isotropic solution ensures the integrability by quadratures of its equations of motion. This extends to contact manifolds a recent result obtained in the context of general symplectic and Poisson manifolds.Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Padrón, Edith. Universidad de La Laguna; EspañaAmerican Institute of Physics2020-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/126256Grillo, Sergio Daniel; Padrón, Edith; Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures; American Institute of Physics; Journal of Mathematical Physics; 61; 1; 1-2020; 1-230022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.5133153info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1909.11393info:eu-repo/semantics/altIdentifier/doi/10.1063/1.5133153info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:39:53Zoai:ri.conicet.gov.ar:11336/126256instacron: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 10:39:53.679CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
title |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
spellingShingle |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures Grillo, Sergio Daniel Hamilton-Jacobi Contact manifolds Integrable systems |
title_short |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
title_full |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
title_fullStr |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
title_full_unstemmed |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
title_sort |
Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures |
dc.creator.none.fl_str_mv |
Grillo, Sergio Daniel Padrón, Edith |
author |
Grillo, Sergio Daniel |
author_facet |
Grillo, Sergio Daniel Padrón, Edith |
author_role |
author |
author2 |
Padrón, Edith |
author2_role |
author |
dc.subject.none.fl_str_mv |
Hamilton-Jacobi Contact manifolds Integrable systems |
topic |
Hamilton-Jacobi Contact manifolds Integrable systems |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper, we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi equation related to these systems. Then, we show that, for a given contact system, the knowledge of what we have called a complete pseudo-isotropic solution ensures the integrability by quadratures of its equations of motion. This extends to contact manifolds a recent result obtained in the context of general symplectic and Poisson manifolds. Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Padrón, Edith. Universidad de La Laguna; España |
description |
A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper, we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi equation related to these systems. Then, we show that, for a given contact system, the knowledge of what we have called a complete pseudo-isotropic solution ensures the integrability by quadratures of its equations of motion. This extends to contact manifolds a recent result obtained in the context of general symplectic and Poisson manifolds. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01 |
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/11336/126256 Grillo, Sergio Daniel; Padrón, Edith; Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures; American Institute of Physics; Journal of Mathematical Physics; 61; 1; 1-2020; 1-23 0022-2488 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/126256 |
identifier_str_mv |
Grillo, Sergio Daniel; Padrón, Edith; Extended Hamilton-Jacobi theory, contact manifolds, and integrability by quadratures; American Institute of Physics; Journal of Mathematical Physics; 61; 1; 1-2020; 1-23 0022-2488 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.5133153 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1909.11393 info:eu-repo/semantics/altIdentifier/doi/10.1063/1.5133153 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Physics |
publisher.none.fl_str_mv |
American Institute of Physics |
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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1844614425420496896 |
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13.070432 |