Abstract
A relation between Hamiltonian structures on polynomial bundles of various degrees is established. Using this relation it is shown that the symplectic form on the space of stationary solutions, previously defined in terms of the Legendre-Ostrogradskii transformation, is identical to the Kirillov form on the corresponding orbit.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 118–127, 1983.
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Reiman, A.G. A unified Hamiltonian system on polynomial bundles, and the structure of stationary problems. J Math Sci 30, 2319–2326 (1985). https://doi.org/10.1007/BF02105350
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DOI: https://doi.org/10.1007/BF02105350