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

Genadi Levin

doi:10.4064/fm939-7-2020

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

Genadi Levin

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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).

Original language	English
Pages (from-to)	49-67
Number of pages	19
Journal	Fundamenta Mathematicae
Volume	254
Issue number	1
DOIs	https://doi.org/10.4064/fm939-7-2020
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 Instytut Matematyczny PAN.

Keywords

Cauchy transform
Herman rings
Rational approximation
Ruelle-Thurston pushforward operator
Transversality

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10.4064/fm939-7-2020

Cite this

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KW - Rational approximation

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KW - Transversality

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

Abstract

Bibliographical note

Keywords

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