Abstract
In this paper we exhibit the Toda lattice equations in a double bracket form which shows they are gradient flow equations (on their isospectral set) on an adjoint orbit of a compact Lie group. Representations for the flows are given and a convexity result associated with a momentum map is proved. Some general properties of the double bracket equations are demonstrated, including a discussion of their invariant subspaces, and their function as a Lie algebraic sorter.
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Communicated by N. Yu. Reshetikhin
Supported in part by NSF Grant DMS-90-02136, NSF PYI Grant DMS-9157556, and a Seed Grant from Ohio State University
Supported in part by AFOSR grant AFOSR-96-0197, by U.S. Army Research Office grant DAAL03-86-K-0171 and by NSF grant CDR-85-00108
Supported in part by NSF Grant DMS-8922699
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Bloch, A.M., Brockett, R.W. & Ratiu, T.S. Completely integrable gradient flows. Commun.Math. Phys. 147, 57–74 (1992). https://doi.org/10.1007/BF02099528
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DOI: https://doi.org/10.1007/BF02099528