Eremenko, Alexandre and Strien, Sebastian van (2011) Rational maps with real multipliers. Transactions of the American Mathematical Society, Vol.363 (No.12). pp. 6453-6463. doi:10.1090/S0002-9947-2011-05308-0 ISSN 0002-9947.

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Abstract

Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Mappings (Mathematics), Julia sets
Journal or Publication Title:	Transactions of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0002-9947
Official Date:	December 2011
Dates:	Date Event December 2011 Published
Volume:	Vol.363
Number:	No.12
Page Range:	pp. 6453-6463
DOI:	10.1090/S0002-9947-2011-05308-0
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	18 December 2015
Date of first compliant Open Access:	18 December 2015
Funder:	National Science Foundation (U.S.) (NSF), Royal Society (Great Britain), Leverhulme Trust (LT)
Grant number:	DMS-0555279 (NSF)

Data sourced from Thomson Reuters' Web of Knowledge

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