Jacobi Metric and Morse Theory of Dynamical Systems

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dc.creatorIzquierdo, A. Alonso
dc.creatorLeon, M. A. Gonzalez
dc.creatorGuilarte, J. Mateos
dc.creatorMayado, M. de la Torre
dc.date2002-12-04
dc.date.accessioned2026-07-07T06:27:20Z
dc.date.available2026-07-07T06:27:20Z
dc.descriptionThe generalization of the Maupertuis principle to second-order Variational Calculus is performed. The stability of the solutions of a natural dynamical system is thus analyzed via the extension of the Theorem of Jacobi. It is shown that the Morse Theory of the trajectories in the dynamical system is identical to the Morse Theory of geodesics in the Jacobi metric, even though the second-variation functionals around the action and the Jacobi length do not coincide. As a representative example, we apply this result to the study of the separatrix solutions of the Garnier System.
dc.description11 pages, 3 figures. Talk delivered at the XI Fall Workshop on Geometry and Physics held at Oviedo, Spain, 2002
dc.identifierhttps://arxiv.org/abs/math-ph/0212017
dc.identifierhttp://arxiv.org/abs/math-ph/0212017
dc.identifierPubl. R. Soc. Mat. Esp. 6 (2004) 81--91
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97388
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.titleJacobi Metric and Morse Theory of Dynamical Systems
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