Fixed points of the Ruelle–Thurston operator and the Cauchy transform
Volume 254 / 2021
Fundamenta Mathematicae 254 (2021), 49-67
MSC: Primary 37F10; Secondary 41A20.
DOI: 10.4064/fm939-7-2020
Published online: 21 December 2020
Abstract
We give necessary and sufficient conditions for a function in a naturally appearing function 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 2020 paper of the author. As an immediate consequence, in Theorem 1 and Lemma 2.2 we revisit Theorem 1 and Lemma 5.2 of Levin (2014).
