Special flow systems with the minimal self-joining property

TL;DR

This paper proves that typical Arnol'd flows possess the minimal self-joining property, enabling classification of their centralizers and factors, advancing understanding of their structural dynamics.

Contribution

It establishes that typical Arnol'd flows have the minimal self-joining property, a significant step in understanding their ergodic and structural properties.

Findings

Typical Arnol'd flows have the minimal self-joining property.

This property allows classification of centralizers and factors.

The results deepen understanding of Arnol'd flows' dynamics.

Abstract

Arnol'd flows are a class of area-preserving flows on surfaces. In this paper, we prove that typical Arnol'd flows have the minimal self-joining property. Consequently, we can classify centralizers and factors of typical Arnol'd flows.