On the fixed points of the Ruelle operator

TL;DR

This paper explores the connection between fixed points of the Ruelle operator on various Banach spaces and Sullivan's conjecture in holomorphic dynamics, providing insights into their relationship.

Contribution

It investigates the existence of fixed points of the Ruelle operator across different Banach spaces in relation to Sullivan's conjecture, offering new theoretical insights.

Findings

Established links between fixed points of the Ruelle operator and Sullivan's conjecture

Provided conditions for the existence of fixed points in various Banach spaces

Enhanced understanding of the operator's role in holomorphic dynamics

Abstract

We discuss the relation between the existence of fixed points of the Ruelle operator acting on different Banach spaces, with Sullivan's conjecture in holomorphic dynamics.