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Please use this identifier to cite or link to this item: http://uvadoc.uva.es/handle/10324/33629
Title: Global versus local superintegrability of nonlinear oscillators
Authors: Anco, S.C.
Ballesteros, A.
Gandarias, M.L.
Issue Date: 2019
Citation: Physics Letters A, to appear (2019)
Abstract: Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals. Therefore, it seems natural to investigate in which sense Lie point symmetries can be used to provide information concerning the superintegrability of a given Hamiltonian system. The two-dimensional oscillator and the central force problem are used as benchmark examples to show that the relationship between standard Lie point symmetries and superintegrability is neither straightforward nor universal. In general, it turns out that super-integrability is not related to either the size or the structure of the algebra of variational dynamical symmetries. Nevertheless, all of the first integrals for a given Hamiltonian system can be obtained through an extension of the standard point symmetry method, which is applied to a superintegrable nonlinear oscillator describing the motion of a particle on a space with non-constant curvature and spherical symmetry.
Peer Review: SI
Language: eng
URI: http://uvadoc.uva.es/handle/10324/33629
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:FM - Artículos de revista

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