Furstenberg's Times 2, Times 3 Conjecture (a Short Survey)

TL;DR

This paper provides a concise survey of Furstenberg's Times 2, Times 3 Conjecture, including key proofs for positive entropy cases and a related theorem, summarizing existing results without introducing new findings.

Contribution

It compiles and explains existing proofs related to Furstenberg's conjecture, offering clarity and comparison without new research contributions.

Findings

Summarizes proofs for positive entropy cases

Includes a simpler related theorem by Lyons

Provides a clear exposition of existing results

Abstract

The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented and proved. This is a survey, no new results are introduced.