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A System of $n=3$ Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: non-symplectic symmetries; bi-Hamiltonian structures;master symmetries; cubic integrals. 
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     author = {Manuel F. Ra\~nada},
     title = {A {System} of $n=3$ {Coupled} {Oscillators} with {Magnetic} {Terms:} {Symmetries} and {Integrals} of {Motion}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2005},
     volume = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a3/}
}
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Manuel F. Rañada. A System of $n=3$ Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a3/

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