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Please use this identifier to cite or link to this item: http://uvadoc.uva.es/handle/10324/33637
Title: Lie–Hamilton systems on curved spaces: A geometrical approach
Authors: Herranz, F.J.
de Lucas, J.
Tobolski, M.
Issue Date: 2017
Description: Producción Científica
Citation: Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 495201
Abstract: A Lie–Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot–Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie–Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.
Peer Review: SI
Language: eng
URI: http://uvadoc.uva.es/handle/10324/33637
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:FM - Artículos de revista

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