On Quadratic Stochastic Operators Corresponding to Cyclic Groups

Abstract

We introduce a new class of quadratic stochastic operators corresponding to cyclic groups. We study the set of fixed points and prove that almost all (w.r.t. Lebesgue measure) trajectories of such operators converge to the center of the simplex. For the cyclic groups of order 2n we show that for any subgroup corresponding quadratic stochastic operator is a regular operator.