BLASCHKE PRODUCTS AND RATIONAL FUNCTIONS WITH SIEGEL DISKS

Title & Authors
BLASCHKE PRODUCTS AND RATIONAL FUNCTIONS WITH SIEGEL DISKS
Katagata, Koh;

Abstract
Let m be a positive integer. We show that for any given real number $\small{{\alpha}\;{\in}\;[0,\;1]}$ and complex number $\small{\mu}$ with $\small{|\mu|{\leq}1}$ which satisfy $\small{e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1}$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier $\small{{\mu}^m}$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\small{\alpha}$. Moreover if the given real number $\small{\alpha}$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier $\small{{\mu}^m}$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.
Keywords
Blaschke product;Siegel disk;
Language
English
Cited by
1.
DYNAMICS OF TRANSCENDENTAL ENTIRE FUNCTIONS WITH SIEGEL DISKS AND ITS APPLICATIONS,;

대한수학회보, 2011. vol.48. 4, pp.713-724
1.
DYNAMICS OF TRANSCENDENTAL ENTIRE FUNCTIONS WITH SIEGEL DISKS AND ITS APPLICATIONS, Bulletin of the Korean Mathematical Society, 2011, 48, 4, 713
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