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Fixed points of the Ruelle–Thurston operator and the Cauchy transform

Volume 254 / 2021

Genadi Levin Fundamenta Mathematicae 254 (2021), 49-67 MSC: Primary 37F10; Secondary 41A20. DOI: 10.4064/fm939-7-2020 Published online: 21 December 2020


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).


  • Genadi LevinInstitute of Mathematics
    Hebrew University of Jerusalem
    Givat Ram, Jerusalem, Israel

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