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Communications in Mathematical Physics

, Volume 139, Issue 2, pp 217–243 | Cite as

Discrete versions of some classical integrable systems and factorization of matrix polynomials

  • Jürgen Moser
  • Alexander P. Veselov
Article

Abstract

Discrete versions of several classical integrable systems are investigated, such as a discrete analogue of the higher dimensional force-free spinning top (Euler-Arnold equations), the Heisenberg chain with classical spins and a new discrete system on the Stiefel manifold. The integrability is shown with the help of a Lax-pair representation which is found via a factorization of certain matrix polynomials. The complete description of the dynamics is given in terms of Abelian functions; the flow becomes linear on a Prym variety corresponding to a spectral curve. The approach is also applied to the billiard problem in the interior of anN-dimensional ellipsoid.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Jürgen Moser
    • 1
  • Alexander P. Veselov
    • 2
  1. 1.Forschungsinstitut für MathematikETH ZürichZürichSwitzerland
  2. 2.Moscow State UniversityMoscowUSSR

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