Rational maps with real multipliers
File(s)0810.2260v1.pdf (156.9 KB)
Accepted version
Author(s)
Eremenko, A
van Strien, S
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.
Date Issued
2011-07-25
Date Acceptance
2009-12-15
Citation
Transactions of the American Mathematical Society, 2011, 363 (12), pp.6453-6463
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.
Subjects
math.DS
math.CV
37F10, 30D05
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2011-07-25