Regularity of some class of nonlinear transformations

TL;DR

This paper proves that quadratic stochastic operators constructed on finite Abelian groups exhibit the property of regularity, contributing to the understanding of their long-term behavior in mathematical and probabilistic contexts.

Contribution

It establishes the regularity of quadratic stochastic operators on finite Abelian groups, a novel result in the study of nonlinear transformations.

Findings

Quadratic stochastic operators on finite Abelian groups are regular.

Regularity holds for all such operators.

Provides a foundation for analyzing long-term dynamics of these operators.

Abstract

In this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.