On the Convex Combination of Volterra Operators

We consider a convex combination of certain Volterra operators defined on the two-dimensional simplex depending on the parameter θ, 0 ≤ θ ≤ 1, and study their trajectory behaviours. We divide the set of the parameter θ into two subsets such that on the first (resp. second) of them the corresponding Volterra operator is a regular (resp. non-ergodic) transformation.