On Dynamics of a Separable Cubic Stochastic Operators

In this paper, we study a class of separable cubic stochastic operators defined on a finite-dimensional simplex. That is, we consider cubic stochastic operators defined as a product of three linear operators defined on a simplex. It is shown that for a separable cubic stochastic operator defined on a two-dimensional simplex, the vertices of the simplex are fixed points. It is also proven that the orbit of a separable cubic stochastic operator converges for any starting point taken from the simplex.