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Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal (1004.3955v1)
Published 22 Apr 2010 in math-ph, math.DS, and math.MP
Abstract: By application of the coinduction method as well as Magri method to the ideal of real Hilbert-Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on the Banach Lie-Poisson spaces which consist of these type of operators. We also discuss their algebraic and analytic properties as well as solve them in dimensions N=2,3,4.
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