A system of coupled oscillators with magnetic terms: symmetries and integrals of motion.
Rañada, Manuel F. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Rañada, Manuel F. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
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SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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