Fixed points of the Ruelle-Thurston operator and the Cauchy transform
Dynamical Systems
2020-07-23 v2 Complex Variables
Abstract
We give necessary and sufficient conditions for a function in a naturally appearing functional space to be a fixed point of the Ruelle-Thurston operator associated to a rational function, see Lemma 2.1. The proof uses essentially a recent [13]. As an immediate consequence, we revisit Theorem 1 and Lemma 5.2 of [11], see Theorem 1 and Lemma 2.2 below.
Cite
@article{arxiv.2002.03430,
title = {Fixed points of the Ruelle-Thurston operator and the Cauchy transform},
author = {Genadi Levin},
journal= {arXiv preprint arXiv:2002.03430},
year = {2020}
}
Comments
To appear in Fundamenta Mathematicae