# A note on directional closing

## TL;DR

This paper demonstrates that certain properties of directional closing and polygonality in dynamical systems are not preserved under conjugacy, challenging assumptions about their invariance.

## Contribution

It reveals that directional closing and polygonality are not closed under conjugacy, providing new insights into their structural properties.

## Key findings

- Directional closing is not closed under conjugacy.
- Polygonality in the sense of Franks-Kra is not closed under conjugacy.
- Implications for the invariance of these properties in dynamical systems.

## Abstract

We show that directional closing in the sense of Guillon-Kari-Zinoviadis and Franks-Kra is not closed under conjugacy. This implies that being polygonal in the sense of Franks-Kra is not closed under conjugacy.