Flows with Ratner's property have discrete essential centralizer

TL;DR

This paper proves that free, ergodic flows with Ratner's property have a countable discrete essential centralizer and are mildly mixing, advancing understanding of their structural properties.

Contribution

It establishes that flows with Ratner's property possess a countable discrete essential centralizer and are mildly mixing, revealing new structural insights.

Findings

Flows with Ratner's property have countable discrete essential centralizer.

Such flows are mildly mixing.

The results connect Ratner's property with flow centralizer structure.

Abstract

We show that a free, ergodic action of $\mathbb{R}$ with (finite) Ratner's property has countable discrete essential centralizer. Moreover we show that such flows are mildly mixing.