Subsequence Rational Ergodicity of Rank-One Transformations

TL;DR

This paper investigates the ergodic properties of rank-one transformations, establishing that they are subsequence boundedly rationally ergodic, but some are not weakly rationally ergodic, revealing nuanced behaviors in ergodic theory.

Contribution

It proves that all rank-one transformations are subsequence boundedly rationally ergodic and identifies the existence of transformations that are not weakly rationally ergodic.

Findings

All rank-one transformations are subsequence boundedly rationally ergodic.

Existence of rank-one transformations that are not weakly rationally ergodic.

Abstract

We show that all rank-one transformations are subsequence boundedly rationally ergodic and that there exist rank-one transformations that are not weakly rationally ergodic.