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dc.contributor.author
Grillo, Sergio Daniel
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dc.contributor.author
Marrero, Juan Carlos
dc.contributor.author
Padrón, Edith
dc.date.available
2022-05-12T16:02:46Z
dc.date.issued
2021-06
dc.identifier.citation
Grillo, Sergio Daniel; Marrero, Juan Carlos; Padrón, Edith; Extended Hamilton-Jacobi Theory, Symmetries and Integrability by Quadratures; Multidisciplinary Digital Publishing Institute; Mathematics; 9; 12; 6-2021; 1-34
dc.identifier.issn
2227-7390
dc.identifier.uri
http://hdl.handle.net/11336/157388
dc.description.abstract
In this paper, we study the extended Hamilton–Jacobi Theory in the context of dynamical systems with symmetries. Given an action of a Lie group G on a manifold M and a G-invariant vector field X on M, we construct complete solutions of the Hamilton–Jacobi equation (HJE) related to X (and a given fibration on M). We do that along each open subset U⊆M, such that π(U) has a manifold structure and π|U:U→π(U), the restriction to U of the canonical projection π:M→M/G, is a surjective submersion. If X|U is not vertical with respect to π|U, we show that such complete solutions solve the reconstruction equations related to X|U and G, i.e., the equations that enable us to write the integral curves of X|U in terms of those of its projection on π(U). On the other hand, if X|U is vertical, we show that such complete solutions can be used to construct (around some points of U) the integral curves of X|U up to quadratures. To do that, we give, for some elements ξ of the Lie algebra g of G, an explicit expression up to quadratures of the exponential curve exp(ξt), different to that appearing in the literature for matrix Lie groups. In the case of compact and of semisimple Lie groups, we show that such expression of exp(ξt) is valid for all ξ inside an open dense subset of g.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Multidisciplinary Digital Publishing Institute
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
Hamilton–Jacobi Theory
dc.subject
Lie group
dc.subject
Symplectic geometry
dc.subject
Integrability by quadratures
dc.subject
First integrals
dc.subject
Quadratures
dc.subject
Reconstruction
dc.subject
Lie group exponential map
dc.subject.classification
Matemática Pura
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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
Extended Hamilton-Jacobi Theory, Symmetries and Integrability by Quadratures
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-03-10T12:05:18Z
dc.journal.volume
9
dc.journal.number
12
dc.journal.pagination
1-34
dc.journal.pais
Suiza
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dc.journal.ciudad
Basilea
dc.description.fil
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. Universidad Nacional de Cuyo; Argentina
dc.description.fil
Fil: Marrero, Juan Carlos. Universidad de La Laguna; España. Consejo Superior de Investigaciones Científicas; España
dc.description.fil
Fil: Padrón, Edith. Universidad de La Laguna; España. Consejo Superior de Investigaciones Científicas; España
dc.journal.title
Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2227-7390/9/12/1357
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.3390/math9121357
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2105.02130
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