  Building on the Renormalization Group (RG) method the beam-beam interaction
in circular colliders is studied. A regularized symplectic RG beam-beam map,
that describes successfully the long-time asymptotic behavior of the original
system has been obtained. The integral of motion possessed by the regularized
RG map has been used to construct the invariant phase space density (stationary
distribution function), and a coupled set of nonlinear integral equations for
the distributions of the two colliding beams has been derived.
