On the flips for a synchronized system

TL;DR

This paper investigates the properties of flips in infinite synchronized systems, demonstrating the existence of infinitely many non-conjugate flips and highlighting limitations in extending these results to coded systems.

Contribution

It establishes that infinite synchronized systems with a flip possess infinitely many non-conjugate flips, revealing a new structural property and its limitations.

Findings

Infinite synchronized systems with a flip have infinitely many non-conjugate flips.

The result does not extend to coded systems.

Highlights structural differences between synchronized and coded systems.

Abstract

It is shown that if an infinite synchronized system has a flip, then it has infinitely many non-conjugate flips, and that the result cannot be extended to the class of coded systems.