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Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders

Volume 261 / 2023

Konstantin Bogdanov Fundamenta Mathematicae 261 (2023), 157-200 MSC: Primary 37F20; Secondary 37F34, 37F10, 37F12. DOI: 10.4064/fm82-11-2022 Published online: 26 January 2023

Abstract

We develop techniques that lay out a basis for generalizations of Thurston’s famous Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider Thurston’s $\sigma $-map acting on a Teichmüller space which is this time infinite-dimensional – and this leads to a completely different theory compared to the classical setting.

We demonstrate our techniques by giving an alternative proof of the result by Markus Förster about the classification of exponential functions with the escaping singular value.

Authors

  • Konstantin BogdanovAix-Marseille Université
    Centrale Marseille
    Institut de Mathématiques de Marseille, UMR 7373
    13453 Marseille, France
    and
    Institute of Mathematics
    Polish Academy of Sciences
    00-656 Warszawa, Poland
    e-mail

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