A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds
- Autores
- Grillo, Sergio Daniel; Padrón, Edith
- Año de publicación
- 2016
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some approaches to a Hamilton–Jacobi Theory for nonholonomic systems). Given a dynamical system, we show that every complete solution of its related Hamilton–Jacobi Equation (HJE) gives rise to a set of first integrals, and vice versa. From that, and in the context of symplectic and Poisson manifolds, a deep connection between the HJE and the (non)commutative integrability notion, and consequently the integrability by quadratures, is established. Moreover, in the same context, we find conditions on the complete solutions of the HJE that also ensures integrability by quadratures, but they are weaker than those related to the (non)commutative integrability. Examples are developed along all the paper in order to illustrate the theoretical results.
Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
Fil: Padrón, Edith. Universidad de La Laguna; España. Consejo Superior de Investigaciones Científicas; España - Materia
-
HAMILTON–JACOBI EQUATIONS
INTEGRABLE SYSTEMS
POISSON MANIFOLD - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/78115
Ver los metadatos del registro completo
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A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifoldsGrillo, Sergio DanielPadrón, EdithHAMILTON–JACOBI EQUATIONSINTEGRABLE SYSTEMSPOISSON MANIFOLDhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some approaches to a Hamilton–Jacobi Theory for nonholonomic systems). Given a dynamical system, we show that every complete solution of its related Hamilton–Jacobi Equation (HJE) gives rise to a set of first integrals, and vice versa. From that, and in the context of symplectic and Poisson manifolds, a deep connection between the HJE and the (non)commutative integrability notion, and consequently the integrability by quadratures, is established. Moreover, in the same context, we find conditions on the complete solutions of the HJE that also ensures integrability by quadratures, but they are weaker than those related to the (non)commutative integrability. Examples are developed along all the paper in order to illustrate the theoretical results.Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Padrón, Edith. Universidad de La Laguna; España. Consejo Superior de Investigaciones Científicas; EspañaElsevier Science2016-12-01info: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/11336/78115Grillo, Sergio Daniel; Padrón, Edith; A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds; Elsevier Science; Journal Of Geometry And Physics; 110; 1-12-2016; 101-1290393-0440CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2016.07.010info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044016301760info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.03121info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:14:02Zoai:ri.conicet.gov.ar:11336/78115instacron: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 10:14:02.654CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
title |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
spellingShingle |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds Grillo, Sergio Daniel HAMILTON–JACOBI EQUATIONS INTEGRABLE SYSTEMS POISSON MANIFOLD |
title_short |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
title_full |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
title_fullStr |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
title_full_unstemmed |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
title_sort |
A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds |
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 EQUATIONS INTEGRABLE SYSTEMS POISSON MANIFOLD |
topic |
HAMILTON–JACOBI EQUATIONS INTEGRABLE SYSTEMS POISSON MANIFOLD |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some approaches to a Hamilton–Jacobi Theory for nonholonomic systems). Given a dynamical system, we show that every complete solution of its related Hamilton–Jacobi Equation (HJE) gives rise to a set of first integrals, and vice versa. From that, and in the context of symplectic and Poisson manifolds, a deep connection between the HJE and the (non)commutative integrability notion, and consequently the integrability by quadratures, is established. Moreover, in the same context, we find conditions on the complete solutions of the HJE that also ensures integrability by quadratures, but they are weaker than those related to the (non)commutative integrability. Examples are developed along all the paper in order to illustrate the theoretical results. Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina Fil: Padrón, Edith. Universidad de La Laguna; España. Consejo Superior de Investigaciones Científicas; España |
description |
In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some approaches to a Hamilton–Jacobi Theory for nonholonomic systems). Given a dynamical system, we show that every complete solution of its related Hamilton–Jacobi Equation (HJE) gives rise to a set of first integrals, and vice versa. From that, and in the context of symplectic and Poisson manifolds, a deep connection between the HJE and the (non)commutative integrability notion, and consequently the integrability by quadratures, is established. Moreover, in the same context, we find conditions on the complete solutions of the HJE that also ensures integrability by quadratures, but they are weaker than those related to the (non)commutative integrability. Examples are developed along all the paper in order to illustrate the theoretical results. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-12-01 |
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/11336/78115 Grillo, Sergio Daniel; Padrón, Edith; A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds; Elsevier Science; Journal Of Geometry And Physics; 110; 1-12-2016; 101-129 0393-0440 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/78115 |
identifier_str_mv |
Grillo, Sergio Daniel; Padrón, Edith; A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds; Elsevier Science; Journal Of Geometry And Physics; 110; 1-12-2016; 101-129 0393-0440 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/j.geomphys.2016.07.010 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044016301760 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.03121 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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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 |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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