Toda flows are extended to a class of unbounded initial conditions with sublinear growth, including η-ensembles from random matrix theory that yield invariant measures.
Sato:Soliton equations as dynamical systems on infinite dimen- sional Grassmann manifold, Suriken Koukyuroku439(1981), 30-46 (http://www.kurims.kyoto-u.ac.jp/en/publi-01.html)
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Toda flow with unbounded initial data
Toda flows are extended to a class of unbounded initial conditions with sublinear growth, including η-ensembles from random matrix theory that yield invariant measures.