Rational maps with real multipliers

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Title: Rational maps with real multipliers
Authors: Eremenko, A
Van Strien, S
Item Type: Journal Article
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.
Issue Date: 25-Jul-2011
Date of Acceptance: 15-Dec-2009
URI: http://hdl.handle.net/10044/1/64739
DOI: https://dx.doi.org/10.1090/S0002-9947-2011-05308-0
ISSN: 0002-9947
Publisher: American Mathematical Society
Start Page: 6453
End Page: 6463
Journal / Book Title: Transactions of the American Mathematical Society
Volume: 363
Issue: 12
Copyright Statement: © 2011 American Mathematical Society.
Keywords: math.DS
37F10, 30D05
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2011-07-25
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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