Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation
- Autores
- Grillo, Sergio Daniel
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown is a section σ:N→M of Π. The standard HJE is obtained when the phase space M is a cotangent bundle T∗Q (with its canonical symplectic form), Π is the canonical projection πQ:T∗Q→Q and the unknown is a closed 1-form dW:Q→T∗Q. The function W is called Hamilton's characteristic function. Coming back to the generalized version, among the solutions of the Π-HJE, a central role is played by the so-called isotropic complete solutions. This is because, if a solution of this kind is known for a given Hamiltonian system, then such a system can be integrated up to quadratures. The purpose of the present paper is to prove that, under mild conditions, an isotropic complete solution exists around almost every point of M. Restricted to the standard case, this gives rise to an alternative proof for the local existence of a complete family of Hamilton's characteristic functions.
Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina - Materia
-
HAMILTON–JACOBI THEORY
INTEGRABLE SYSTEMS
SYMPLECTIC GEOMETRY - 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:11336/126678
Ver los metadatos del registro completo
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Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equationGrillo, Sergio DanielHAMILTON–JACOBI THEORYINTEGRABLE SYSTEMSSYMPLECTIC GEOMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown is a section σ:N→M of Π. The standard HJE is obtained when the phase space M is a cotangent bundle T∗Q (with its canonical symplectic form), Π is the canonical projection πQ:T∗Q→Q and the unknown is a closed 1-form dW:Q→T∗Q. The function W is called Hamilton's characteristic function. Coming back to the generalized version, among the solutions of the Π-HJE, a central role is played by the so-called isotropic complete solutions. This is because, if a solution of this kind is known for a given Hamiltonian system, then such a system can be integrated up to quadratures. The purpose of the present paper is to prove that, under mild conditions, an isotropic complete solution exists around almost every point of M. Restricted to the standard case, this gives rise to an alternative proof for the local existence of a complete family of Hamilton's characteristic functions.Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaElsevier Science2020-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/126678Grillo, Sergio Daniel; Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation; Elsevier Science; Journal Of Geometry And Physics; 148; 103544; 2-2020; 1-110393-0440CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044019302256info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2019.103544info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.02280v1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:03Zoai:ri.conicet.gov.ar:11336/126678instacron: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 10:37:03.851CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
title |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
spellingShingle |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation Grillo, Sergio Daniel HAMILTON–JACOBI THEORY INTEGRABLE SYSTEMS SYMPLECTIC GEOMETRY |
title_short |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
title_full |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
title_fullStr |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
title_full_unstemmed |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
title_sort |
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation |
dc.creator.none.fl_str_mv |
Grillo, Sergio Daniel |
author |
Grillo, Sergio Daniel |
author_facet |
Grillo, Sergio Daniel |
author_role |
author |
dc.subject.none.fl_str_mv |
HAMILTON–JACOBI THEORY INTEGRABLE SYSTEMS SYMPLECTIC GEOMETRY |
topic |
HAMILTON–JACOBI THEORY INTEGRABLE SYSTEMS SYMPLECTIC GEOMETRY |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown is a section σ:N→M of Π. The standard HJE is obtained when the phase space M is a cotangent bundle T∗Q (with its canonical symplectic form), Π is the canonical projection πQ:T∗Q→Q and the unknown is a closed 1-form dW:Q→T∗Q. The function W is called Hamilton's characteristic function. Coming back to the generalized version, among the solutions of the Π-HJE, a central role is played by the so-called isotropic complete solutions. This is because, if a solution of this kind is known for a given Hamiltonian system, then such a system can be integrated up to quadratures. The purpose of the present paper is to prove that, under mild conditions, an isotropic complete solution exists around almost every point of M. Restricted to the standard case, this gives rise to an alternative proof for the local existence of a complete family of Hamilton's characteristic functions. Fil: Grillo, Sergio Daniel. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Universidad Nacional de Cuyo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina |
description |
Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown is a section σ:N→M of Π. The standard HJE is obtained when the phase space M is a cotangent bundle T∗Q (with its canonical symplectic form), Π is the canonical projection πQ:T∗Q→Q and the unknown is a closed 1-form dW:Q→T∗Q. The function W is called Hamilton's characteristic function. Coming back to the generalized version, among the solutions of the Π-HJE, a central role is played by the so-called isotropic complete solutions. This is because, if a solution of this kind is known for a given Hamiltonian system, then such a system can be integrated up to quadratures. The purpose of the present paper is to prove that, under mild conditions, an isotropic complete solution exists around almost every point of M. Restricted to the standard case, this gives rise to an alternative proof for the local existence of a complete family of Hamilton's characteristic functions. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-02 |
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/11336/126678 Grillo, Sergio Daniel; Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation; Elsevier Science; Journal Of Geometry And Physics; 148; 103544; 2-2020; 1-11 0393-0440 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/126678 |
identifier_str_mv |
Grillo, Sergio Daniel; Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation; Elsevier Science; Journal Of Geometry And Physics; 148; 103544; 2-2020; 1-11 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/url/https://www.sciencedirect.com/science/article/pii/S0393044019302256 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2019.103544 info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.02280v1 |
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/zip application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
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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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