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Univalent wandering domains in the Eremenko-Lyubich class

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Abstract

We use the Folding Theorem of [Bis15] to construct an entire function f in class \({\cal B}\) and a wandering domain U of f such that f restricted to fn (U) is univalent, for all n ≥ 0. The components of the wandering orbit are bounded and surrounded by the postcritical set.

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Authors and Affiliations

  1. Departament de Matemàtiques i Informàtica, Institut de Matemàtiques de la Universitat de Barcelona and Barcelona Graduate School of Mathematics, Gran Via 585, 08007, Barcelona, Catalonia

    Núria Fagella & Xavier Jarque

  2. California Institute of Technology, 1200 E California Blvd, Pasadena, CA, 91125, USA

    Kirill Lazebnik

Authors
  1. Núria Fagella
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  2. Xavier Jarque
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  3. Kirill Lazebnik
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Corresponding author

Correspondence to Kirill Lazebnik.

Additional information

The first and second authors were partially supported by the Spanish grant MTM2017-86795-C3-3-P, the Maria de Maeztu Excellence Grant MDM-2014-0445, and grant 2017SGR1374 from the Generalitat de Catalunya.

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Fagella, N., Jarque, X. & Lazebnik, K. Univalent wandering domains in the Eremenko-Lyubich class. JAMA 139, 369–395 (2019). https://doi.org/10.1007/s11854-027-0079-x

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  • DOI: https://doi.org/10.1007/s11854-027-0079-x

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