Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice

We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem...

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Veröffentlicht in:Physics letters. A Jg. 206; H. 3; S. 153 - 161
1. Verfasser: Suris, Yuri B.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 09.10.1995
ISSN:0375-9601, 1873-2429
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Abstract We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for both maps.
AbstractList We introduce two new discretizations of the Toda lattice related to the qd algorithm. They are demonstrated to belong to the same hierarchy as the continuous-time system, and to exemplify the general scheme for symplectic maps on Lie algebras with r-matrix Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for both maps.
Author Suris, Yuri B.
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  email: suris@mathematik.uni-bremen.de
  organization: Centre for Complex Systems and Visualization, University of Bremen, Postfach 330 440, 28334 Bremen, Germany
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