Poisson structure and invariant manifolds on Lie groups
نویسندگان
چکیده
For a discrete mechanical system on a Lie group G determined by a (reduced) Lagrangian we define a Poisson structure via the pull-back of the Lie-Poisson structure on g∗ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group G of the canonical discrete Lagrange 2-form ωL on G×G. Its symplectic leaves then become dynamically invariant manifolds for the reduced discrete system.
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تاریخ انتشار 2000