Alexandre Eremenko, Sebastian van Strien
Published 2008-10-13Version 1
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.
Comments: 16 pages 1 figure
Journal: Trans. AMS, 363, 12 (2011) 6453-6463
No entire function with real multipliers in class S
A note on repelling periodic points for meromorphic functions with bounded set of singular values
On the spherical derivative of a rational function
![QR code for arXiv:0810.2260 [math.DS]](http://oss.arxitics.com/images/favicon.svg)