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dc.contributor.authorCariñena Marzo, José F.
dc.contributor.authorGràcia Sabaté, Francesc Xavier
dc.contributor.authorMarmo, Giuseppe
dc.contributor.authorMartínez Fernandez, Eduardo
dc.contributor.authorMuñoz Lecanda, Miguel Carlos
dc.contributor.authorRomán Roy, Narciso
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationCariñena, J.F., Gràcia, Xavier, Marmo, G., Martínez, E., Muñoz-Lecanda, Miguel C., Roman-Roy, N. Structural aspects of Hamilton–Jacobi theory. "International journal of geometric methods in modern physics", 1 Febrer 2016, vol. 13, núm. 2, p. 1-26.
dc.descriptionThe final publication is available at Springer via
dc.description.abstractIn our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton–Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (‘slicing vector fields’) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton– Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.
dc.format.extent26 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Àlgebra lineal i multilineal
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshHamiltonian systems
dc.subject.otherHamilton-Jacobi equation
dc.subject.otherslicing vector field
dc.subject.othercomplete solution
dc.subject.otherconstant of the motion
dc.titleStructural aspects of Hamilton–Jacobi theory
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorCariñena, J.F.; Gràcia, Xavier; Marmo, G.; Martínez, E.; Muñoz-Lecanda, Miguel C.; Roman-Roy, N.
upcommons.citation.publicationNameInternational journal of geometric methods in modern physics

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