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Prescribing the postsingular dynamics of meromorphic functions

Bishop, Christopher J. and Lazebnik, Kirill (2019) Prescribing the postsingular dynamics of meromorphic functions. Mathematische Annalen, 375 (3-4). pp. 1761-1782. ISSN 0025-5831. https://resolver.caltech.edu/CaltechAUTHORS:20191114-154132017

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Abstract

We show that any dynamics on any discrete planar sequence S can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small perturbations of S. This work is motivated by an analogous result of DeMarco et al. (Mathematische Annalen, 2018) for finite S in the rational setting. The proof contains a method for constructing meromorphic functions with good control over both the postsingular set of f and the geometry of f, using the Folding Theorem of Bishop (Acta Math 214(1):1–60, 2015) and a classical fixpoint theorem (Tychonoff in Math Ann 111(1):767–776, 1935).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00208-019-01869-6DOIArticle
https://arxiv.org/abs/1807.04581arXivDiscussion Paper
ORCID:
AuthorORCID
Lazebnik, Kirill0000-0001-8963-4410
Additional Information:© 2019 Springer-Verlag GmbH Germany, part of Springer Nature. First Online: 04 July 2019. Christopher J. Bishop is supported partially by National Science Foundation Grant DMS 16-08577. The authors would like to thank the anonymous referees for their suggestions which have led to an improved version of the paper.
Funders:
Funding AgencyGrant Number
NSFDMS 16-08577
Issue or Number:3-4
Classification Code:Mathematics Subject Classification: 30D05; 37F10; 30D30
Record Number:CaltechAUTHORS:20191114-154132017
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191114-154132017
Official Citation:Bishop, C.J. & Lazebnik, K. Math. Ann. (2019) 375: 1761. https://doi.org/10.1007/s00208-019-01869-6
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99852
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Nov 2019 02:59
Last Modified:15 Nov 2019 02:59

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