# Joint coboundaries

## TL;DR

This paper investigates the conditions under which a function is a coboundary for a set of maps and when it is a coboundary for all maps in that set, contributing to the understanding of coboundary properties in dynamical systems.

## Contribution

It provides new criteria for when a function is a coboundary for individual or all maps within a set of transformations.

## Key findings

- Characterization of functions that are coboundaries for specific maps
- Conditions for a function to be a coboundary for all maps in a set
- Theoretical framework for coboundary analysis in dynamical systems

## Abstract

We ask under what conditions on the function $f$, and a set of maps $\mathcal T$, it is the case that $f$ is a coboundary for some map in $\mathcal T$. We also consider for a function $f$, and a set of maps $\mathcal T$, when we have $f$ being a coboundary for all the maps in $\mathcal T$.