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On invariance of order and the area property for finite-type entire functions
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Epstein, Adam L. and Rempe-Gillen, Lasse (2015) On invariance of order and the area property for finite-type entire functions. Annales Academiæ Scientiarum Fennicæ, 40 . pp. 573-599. doi:10.5186/aasfm.2015.4034 ISSN 1798-2383.
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Official URL: https://doi.org/10.5186/aasfm.2015.4034
Abstract
Let f : C → C be an entire function that has only finitely many critical and asymptotic values. Up totopological equivalence, the function f is determined by combinatorial information, more precisely by an infinite graph known as a line-complex. In this note, we discuss the natural question whether the order of growth of an entire function is determined by this combinatorial information. The search for conditions that imply a positive answer to this question leads us to the area property, which turns out to be related to many interesting and important questions in conformal dynamics and function theory. These include a conjecture of Eremenko and Lyubich, the measurable dynamics of entire functions, and push forwards of quadratic differentials. We also discuss evidence that invariance of order and the area property fail in general.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Functions, Entire, Quadratic differentials | ||||||
Journal or Publication Title: | Annales Academiæ Scientiarum Fennicæ | ||||||
Publisher: | Suomalainen Tiedeakatemia | ||||||
ISSN: | 1798-2383 | ||||||
Official Date: | 1 January 2015 | ||||||
Dates: |
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Volume: | 40 | ||||||
Page Range: | pp. 573-599 | ||||||
DOI: | 10.5186/aasfm.2015.4034 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Copyright Holders: | © 2015 by Academia Scientiarum Fennica | ||||||
Date of first compliant deposit: | 4 April 2019 | ||||||
Date of first compliant Open Access: | 4 April 2019 | ||||||
RIOXX Funder/Project Grant: |
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