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http://dx.doi.org/10.4134/BKMS.2011.48.4.713

DYNAMICS OF TRANSCENDENTAL ENTIRE FUNCTIONS WITH SIEGEL DISKS AND ITS APPLICATIONS  

Katagata, Koh (Ichinoseki National College of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 713-724 More about this Journal
Abstract
We study the dynamics of transcendental entire functions with Siegel disks whose singular values are just two points. One of the two singular values is not only a superattracting fixed point with multiplicity more than two but also an asymptotic value. Another one is a critical value with free dynamics under iterations. We prove that if the multiplicity of the superattracting fixed point is large enough, then the restriction of the transcendental entire function near the Siegel point is a quadratic-like map. Therefore the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality. As its applications, the logarithmic lift of the above transcendental entire function has a wandering domain whose shape looks like a Siegel disk of a quadratic polynomial.
Keywords
Siegel disks; wandering domains;
Citations & Related Records
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