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First Integrals of the Full Symmetric Toda System as Vector Fields on SOn(R)

Extends the known equivalence between the full symmetric Toda system and an ODE on the orthogonal group to the system's first integrals, and represents the Lie algebra of B+-invariant functions on the dual of sl_n(R) by vector fields on SO_n(R).

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Full symmetric Toda system and vector fields on the group SOn(R)

A mathematical-physics study of the full symmetric Toda system - a Hamiltonian integrable system on the space of traceless real symmetric matrices - and its relationship to vector fields on the ortho…