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


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.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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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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