An infinitedimensional Hamiltonian system on projective Hilbert space
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 by Anthony M. Bloch PDF
 Trans. Amer. Math. Soc. 302 (1987), 787796 Request permission
Abstract:
We consider here the explicit integration of a Hamiltonian system on infinitedimensional complex projective space. The Hamiltonian, which is the restriction of a linear functional to this projective space, arises in the problem of line fitting in complex Hilbert space (or, equivalently, the problem of functional approximation) or as the expectation value of a model quantum mechanical system. We formulate the system here as a Lax system with parameter, showing how this leads to an infinite set of conserved integrals associated with the problem and to an explicit formulation of the flow in actionangle form via an extension of some work of J. Moser. In addition, we find the algebraic curve naturally associated with the system.References

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Additional Information
 © Copyright 1987 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 302 (1987), 787796
 MSC: Primary 58F05; Secondary 58F07, 70H05, 81C99
 DOI: https://doi.org/10.1090/S00029947198708916475
 MathSciNet review: 891647