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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/126256
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/126256
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network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-22T12:12:15Zoai: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:34982025-10-22 12:12:15.45CONICET 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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score 12.982451

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