Abstract
Let G=KL and g=k+l be Lie group and Lie algebra decompositions. This identifies k owith l *. Any G-invariant function, f, on g *induces by restriction a function f|k o=l *. We prove a formula which says that the integral curve through α∈k ois obtained as b(t)α, where a(t)=exp tξ with ξ=L f (α),
where (*) is the KL decomposition and where L f : g * → g is the Legendre transform. This generalizes a formula of Symes for the generalized Toda lattice.
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Guillemin, V., Sternberg, S. On the method of symes for integrating systems of the toda type. Lett Math Phys 7, 113–115 (1983). https://doi.org/10.1007/BF00419928
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DOI: https://doi.org/10.1007/BF00419928