It is shown that the factorization relation on simple Lie groups with stand
ard Poisson Lie structure restricted to Coxeter symplectic leaves gives an
integrable dynamical system. This system can be regarded as a discretizatio
n of the Toda flow. In case of SLn the integrals of the factorization dynam
ics are integrals of the relativistic Toda system. A substantial part of th
e paper is devoted to the description of symplectic leaves in simple comple
x Lie groups, its Borel subgroups and their doubles.