Abstract:
The properties of a system of n=3 coupled oscillators with linear terms in the velocities (magnetic terms) depending in two parameters are studied. We proved the existence of a bi-Hamiltonian structure arising from a non-symplectic symmetry, as well the existence of master symmetries and additional integrals of motion (weak superintegrability) for certain particular values of the parameters.
Citation:
Manuel F. Rañada, “A System of n=3 Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion”, SIGMA, 1 (2005), 004, 7 pp.
\Bibitem{Ran05}
\by Manuel F. Ra{\~n}ada
\paper A System of $n=3$ Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion
\jour SIGMA
\yr 2005
\vol 1
\papernumber 004
\totalpages 7
\mathnet{http://mi.mathnet.ru/sigma4}
\crossref{https://doi.org/10.3842/SIGMA.2005.004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2173591}
\zmath{https://zbmath.org/?q=an:1093.37024}
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This publication is cited in the following 5 articles:
Alfonso Blasco, Ivan Gutierrez-Sagredo, Francisco J Herranz, “Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system”, Nonlinearity, 36:2 (2023), 1143
M. N. Hounkonnou, M. J. Landalidji, M. Mitrovic, “Hamiltonian dynamics of a spaceship in Alcubierre and Gödel metrics: Recursion operators and underlying master symmetries”, Theoret. and Math. Phys., 212:1 (2022), 1001–1018
Mahouton Norbert Hounkonnou, Mahougnon Justin Landalidji, Melanija Mitrović, “Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds”, Universe, 8:4 (2022), 247
M. N. Hounkonnou, M. J. Landalidji, M. Mitrović, “Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures”, Theoret. and Math. Phys., 207:3 (2021), 751–769
Jose F. Cariñena, Manuel F. Rañada, “Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem”, SIGMA, 12 (2016), 010, 16 pp.
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