The dynamics of doubly stochastic operators on finite dimensional   simplex
  We define a doubly stochastic operator on a finite dimensional simplex and study the limit behavior of the trajectories under doubly stochastic operators. We prove that except for certain points, the trajectory of a point, under the doubly stochastic operator, tends to the center of the simplex. 
Farruh Shahidi and Rasul Ganikhodzhaev
math.DS