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Geometric location of periodic points of 2-ramified power series
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-7825-4428
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-0510-6782
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we study the geometric location of periodic points of power series defined over fields of prime characteristic p. More specifically, we find a lower bound for the absolute value of all periodic points in the open unit disk of minimal period pn of 2-ramified power series. We prove that this bound is optimal for a large class of power series. Our main technical result is a computation of the first significant terms of the pnth iterate of 2-ramified power series. As a by-product we obtain a self-contained proof of the characterization of 2-ramified power series.

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Mathematics
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URN: urn:nbn:se:lnu:diva-64440OAI: oai:DiVA.org:lnu-64440DiVA: diva2:1099114
Available from: 2017-05-29 Created: 2017-05-29 Last updated: 2017-06-01

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Lindahl, Karl-OlofNordqvist, Jonas
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