On some questions of V.I. Arnold on the stochasticity of geometric and arithmetic progressions

Abstract

In some of his final papers, V.I. Arnold studied pseudorandomness properties of finite deterministic sequences, which he measured in terms of their "stochasticity parameter". In the present paper we illustrate the background in probability theory and number theory of some of his considerations, and give answers to some of the questions raised in his papers.

arXiv comment22 pages. A significantly shortened version of this manuscript (14 pages) has been accepted for publication in Nonlinearity