Integrable Lagrangian correspondences and the factorization of matrix polynomials
type: Item
instance of: scholarly article
title: Integrable Lagrangian correspondences and the factorization of matrix polynomials
zbMATH Open document ID: 0731.58034
DOI: 10.1007/BF01079590
publication date: 1991-01-01T00:00:00Z
review text: This paper studies integrable Lagrangian systems with discrete time. The isospectral transformation method is used. In this method the factorization of matrix polynomials is essential. The method is demonstrated with some examples of integrable discrete systems. They are the stationary problems for classical Heisenberg's chain and its generalization to the case where the variable takes values in appropriate homogeneous spaces. For the group O(N), the discrete analog of Euler- Arnold's problem of motion of a multidimensional rigid body is obtained. Another class of problems are billiards in regions of spaces of constant curvature, restricted by corresponding conic sections.
reviewed by: Zhongheng Guo
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 4209142
zbMATH Keywords: integrable Lagrangian systems
zbMATH Keywords: discrete time
zbMATH Keywords: isospectral transformation
zbMATH Keywords: factorization of matrix polynomials
zbMATH Keywords: billiards
author: A. P. Veselov
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4209142