Boundary behavior and rigidity of semigroups of holomorphic mappings
  In this paper we give some quantative characteristics of boundary asymptotic behavior of semigroups of holomorphic self-mappings of the unit disk including the limit curvature of their trajectories at the boundary Denjoy--Wolff point. This enable us to establish an asymptotic rigidity property for semigroups of parabolic type. 
Mark Elin and David Shoikhet
math.CV