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  • Geometry of real forms of the complex Neumann system
    Novak, Tina, 1977-
    In the paper, we study real forms of the complex generic Neumann system. We prove that the real forms are completely integrable Hamiltonian systems. The complex Neumann system is an example of the ... more general Mumford system. The Mumford system is characterized by the Lax pair $(L^{\mathbb C}(\lambda), M^{\mathbb C}(\lambda))$ of $2 \times 2$ matrices, where $L^{\mathbb C}(\lambda)=\left[\begin{matrix} V^{\mathbb C}(\lambda) & W^{\mathbb C}(\lambda) \\ U^{\mathbb C}(\lambda) & -V^{\mathbb C}(\lambda) \end{matrix}\right]$ and $U^{\mathbb C}(\lambda)$, $V^{\mathbb C}(\lambda)$, $W^{\mathbb C}(\lambda)$ are suitable polynomials. The topology of a regular level set of the moment map of a real form is determined by the positions of the roots of the suitable real form of $U^{\mathbb C}(\lambda)$, with respect to the position of the values of suitable parameters of the system. For two families of the real forms of the complex Neumann system, we describe the topology of the regular level set of the moment map. For one of these two families the level sets are noncompact In the paper, we also give the formula which provides the relation between two systems of the first integrals in involution of the Neumann system. One of these systems is obtained from the Lax pair of the Mumford type, while the second is obtained from the Lax pair whose matrices are of dimension $(n+1)\times(n+1)$.
    Vir: Journal of nonlinear mathematical physics. - ISSN 1402-9251 (Vol. 23, nr. 1, Jan. 2016, str. 74-91)
    Vrsta gradiva - članek, sestavni del
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 14429979
    DOI

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