The level manifold of a generalized Toda equation hierarchy

Nakamura, Yoshimasa

doi:10.1090/S0002-9947-1992-1062867-6

The level manifold of a generalized Toda equation hierarchy
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Trans. Amer. Math. Soc. 333 (1992), 83-94 Request permission

Abstract:

The finite nonperiodic Toda lattice equation induces a linear one-parameter flow on a space of rational functions. The level manifold of the Toda equation hierarchy is shown to be a product of lines. Our main results establish a generalization of this Toda hierarchy which will be called the cyclic-Toda hierarchy. It is proved that the cyclic-Toda hierarchy is completely integrable and its level manifold is diffeomorphic to a disjoint union of cylinders.

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