Letters in Mathematical Physics

, Volume 7, Issue 2, pp 113–115

On the method of symes for integrating systems of the toda type

  • V. Guillemin
  • S. Sternberg

DOI: 10.1007/BF00419928

Cite this article as:
Guillemin, V. & Sternberg, S. Lett Math Phys (1983) 7: 113. doi:10.1007/BF00419928


Let G=KL and g=k+l be Lie group and Lie algebra decompositions. This identifies kowith l*. Any G-invariant function, f, on g*induces by restriction a function f|ko=l*. We prove a formula which says that the integral curve through α∈kois obtained as b(t)α, where a(t)=exp tξ with ξ=Lf(α),
$$\left( * \right){\text{ }}a\left( t \right) = b\left( t \right)c\left( t \right)$$
where (*) is the KL decomposition and where Lf: g*g is the Legendre transform. This generalizes a formula of Symes for the generalized Toda lattice.

Copyright information

© D. Reidel Publishing Company 1983

Authors and Affiliations

  • V. Guillemin
    • 1
  • S. Sternberg
    • 2
    • 3
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Harvard UniversityCambridgeUSA
  3. 3.University of Tel AvivTel AvivIsrael

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