Geometric constructions of Toda and periodic Toda chains

A geometrical and neat framework is established to derive both Toda and periodic Toda systems from the geodesics of symmetric spaces. The counterpart of the Iwasawa decomposition of a semisimple Cie group in the case of a loop group is also derived. By these, we get a Lie subalgebra with Lie bracket [,](R), and the corresponding Poisson bracket {,}(R) in gives the Hamiltonian form of the periodic Toda chains.Physics, MultidisciplinarySCI(E)中国科学引文数据库(CSCD)0ARTICLE3289-2942