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dc.contributor.author
Grillo, Sergio Daniel
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dc.date.available
2021-02-25T19:16:44Z
dc.date.issued
2020-02
dc.identifier.citation
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
dc.identifier.issn
0393-0440
dc.identifier.uri
http://hdl.handle.net/11336/126678
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier Science
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
HAMILTON–JACOBI THEORY
dc.subject
INTEGRABLE SYSTEMS
dc.subject
SYMPLECTIC GEOMETRY
dc.subject.classification
Matemática Aplicada
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-02-22T12:50:31Z
dc.journal.volume
148
dc.journal.number
103544
dc.journal.pagination
1-11
dc.journal.pais
Países Bajos
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dc.journal.ciudad
Amsterdam
dc.description.fil
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
dc.journal.title
Journal Of Geometry And Physics
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044019302256
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1016/j.geomphys.2019.103544
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.02280v1
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