Investigation of the statistical properties of a dynamic system generated by number-theoretic endomorphisms

Abstract

© Published under licence by IOP Publishing Ltd. Mathematical modeling uses a wide variety of mathematical methods and concepts, in particular, an ergodic theory that studies statistical properties of motions in measure spaces (dynamic systems). The article is devoted to a further study of the statistical properties of a dynamic system generated by number-theoretic endomorphisms. An estimate of the convergence rate in the central limit theorem for sums of functions from number-theoretic endomorphisms trajectories is obtained. The obtained results may be of interest to practitioners using the theory of dynamic systems and specialists in number theory.