2024-03-28T20:25:56Zhttp://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/336372021-06-24T07:21:41Zcom_10324_22154com_10324_954com_10324_894col_10324_22155
Lie–Hamilton systems on curved spaces: A geometrical approach
Herranz, F.J.
Lucas Veguillas, Javier de
Tobolski, M.
Producción Científica
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.
2018-12-27T16:33:08Z
2018-12-27T16:33:08Z
2017
info:eu-repo/semantics/article
Journal of Physics A: Mathematical and Theoretical, vol. 50 (2017) 495201
http://uvadoc.uva.es/handle/10324/33637
495201
eng
info:eu-repo/semantics/openAccess
SI