Centralizer and liftable centralizer of special flows over rotations

TL;DR

This paper investigates the liftable centralizer in special flows over irrational rotations, revealing cases where it is trivial despite the flow's rigidity, especially under piecewise constant roof functions.

Contribution

It demonstrates the existence of rigid special flows over rotations with trivial liftable centralizer, highlighting new insights into their symmetry properties.

Findings

Existence of rigid special flows with trivial liftable centralizer

Liftable centralizer can be trivial even in rigid flows

Special flows over rotations with piecewise constant roof functions

Abstract

The liftable centralizer for special flows over irrational rotations is studied. It is shown that there are such flows under piecewise constant roof functions which are rigid and whose liftable centralizer is trivial.