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Conformal Geometry and Dynamics

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Combinatorics of criniferous entire maps with escaping critical values


Author: Leticia Pardo-Simón
Journal: Conform. Geom. Dyn. 25 (2021), 51-78
MSC (2020): Primary 37F10; Secondary 30D05
DOI: https://doi.org/10.1090/ecgd/358
Published electronically: June 21, 2021
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Abstract: A transcendental entire function is called criniferous if every point in its escaping set can eventually be connected to infinity by a curve of escaping points. Many transcendental entire functions with bounded singular set have this property, and this class has recently attracted much attention in complex dynamics. In the presence of escaping critical values, these curves break or split at critical points. In this paper, we develop combinatorial tools that allow us to provide a complete description of the escaping set of any criniferous function without asymptotic values on its Julia set. In particular, our description precisely reflects the splitting phenomenon. This combinatorial structure provides the foundation for further study of this class of functions. For example, we use these results in another paper to give the first full description of the topological dynamics of a class of transcendental entire maps with unbounded postsingular set.


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Additional Information

Leticia Pardo-Simón
Affiliation: Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland
ORCID: 0000-0003-4039-5556
Email: l.pardo-simon@impan.pl

Received by editor(s): October 23, 2020
Published electronically: June 21, 2021
Article copyright: © Copyright 2021 American Mathematical Society