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- W2010435836 abstract "A geometrical description of continuous and discrete versions of the Neumann oscillator in terms of a loop group framework is investigated. It is shown that the continuous Neumann oscillator can be integrated by the Riemann–Hilbert factorization on the “twisted” loop group of O(3), LO(3). The solution of the problem is given in terms of a special class of flows on the quotient space LO(3)/LO(3)+ where LO(3)+ is a subgroup of positive loops in LO(3). It is also shown that the Moser–Veselov algorithm for integrating a discrete version of the Neumann oscillator (Heisenberg XYZ chain) is induced by a discrete flow in this space. The flow can be explicitly integrated by solving the matrix Riccati equation. In both cases, discrete and continuous, conservation laws are derived from time invariance of a relation that holds for coefficients of the Fourier expansion of the flows." @default.
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- W2010435836 date "1999-10-01" @default.
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- W2010435836 title "A loop group approach to the C. Neumann problem and Moser–Veselov factorization" @default.
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- W2010435836 doi "https://doi.org/10.1063/1.533013" @default.
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