# Transfer operators, atomic decomposition and the Bestiary

## TL;DR

This paper extends the application of atomic decomposition techniques to a broad class of expanding dynamical systems, demonstrating the quasi-compactness of transfer operators on Besov spaces.

## Contribution

It provides a comprehensive list of systems where atomic decomposition results can be applied, advancing the understanding of transfer operators in dynamical systems.

## Key findings

- Quasi-compactness of transfer operators on Besov spaces established
- Applicable to numerous expanding dynamical systems
- Enhances analytical tools for studying transfer operators

## Abstract

Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov spaces of measure spaces with a good grid.