Square Entropy and Uniform n-to-1 Bernoulli Transformations

TL;DR

This paper introduces the concept of square entropy and demonstrates that n-to-1 full zip shift maps are intrinsically ergodic, providing a new way to characterize uniform n-to-1 Bernoulli transformations.

Contribution

It defines square entropy and proves its role in characterizing uniform n-to-1 Bernoulli transformations, extending the understanding of ergodic properties in symbolic dynamics.

Findings

n-to-1 full zip shift maps are intrinsically ergodic

Square entropy characterizes uniform n-to-1 Bernoulli transformations

Extension of Bernoulli transformations analyzed

Abstract

In this paper, we define the so-called square entropy and prove that n-to-1 full zip shift maps are intrinsically ergodic. Furthermore, we show that square entropy characterizes uniform n-to-1 transformations of $(m,l)$-Bernoulli type that are extended Bernoulli transformations.