  We analyze dynamics of the FRW models with global rotation in terms of
dynamical system methods. We reduce dynamics of these models to the FRW models
with some fictitious fluid which scales like radiation matter. This fluid
mimics dynamically effects of global rotation. The significance of the global
rotation of the Universe for the resolution of the acceleration and horizon
problems in cosmology is investigated. It is found that dynamics of the
Universe can be reduced to the two-dimensional Hamiltonian dynamical system.
Then the construction of the Hamiltonian allows for full classification of
evolution paths. On the phase portraits we find the domains of cosmic
acceleration for the globally rotating universe as well as the trajectories for
which the horizon problem is solved. We show that the FRW models with global
rotation are structurally stable. This proves that the universe acceleration is
due to the global rotation. It is also shown how global rotation gives a
natural explanation of the empirical relation between angular momentum for
clusters and superclusters of galaxies. The relation $J \sim M^2$ is obtained
as a consequence of self similarity invariance of the dynamics of the FRW model
with global rotation. In derivation of this relation we use the Lie group of
symmetry analysis of differential equation.
