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The second Hamiltonian structure for the periodic Toda lattice

Published online by Cambridge University Press:  14 November 2011

Gloria Marí Beffa
Gloria Marí Beffa
Affiliation:
Department of Mathematics, University of Wisconsin at Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706, U.S.A.
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Abstract

In this paper we study the Poisson geometry of the second Hamiltonian structure for the periodic N Toda lattice, around a certain family of singularities. We show that their singular leaves are not isolated and that the regular codimension of the leaves at points of this kind is always equal to three. This result is based on a rather unexpected result about a certain Toeplitz matrix.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 3 , 1997 , pp. 547 - 566
Copyright
Copyright © Royal Society of Edinburgh 1997

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