Slope problem for trajectories of holomorphic semigroups in the unit   disc
  It has been an open problem for about ten years whether every trajectory of a parabolic one-parameter semigroup in the unit disk tends to the Denjoy-Wolff point with a definite (and common for all trajectories) slope. In this paper, we give the negative answer to this question. 
Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk
math.CV math.DS