Epicycloids and Blaschke products

Chunlei Cao; Alastair Fletcher; Zhuan Ye

doi:10.1080/10236198.2017.1341499

Epicycloids and Blaschke products

Chunlei Cao
, Alastair Fletcher^*
, Zhuan Ye

^*此作品的通讯作者

数学学院

Northern Illinois University
University of North Carolina at Wilmington

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree d polynomials is an epicycloid with d - 1 cusps. The interior of the epicycloid gives the polynomials of the form z^d +c which have an attracting fixed point. We prove an analogous result for unicritical Blaschke products: in the parameter space of degree d unicritical Blaschke products, the parabolic functions are parameterized by an epicycloid with d − 1 cusps and inside this epicycloid are the parameters which give rise to maps having an attracting fixed point in the unit disk. We further study in more detail the case when d = 2 in which every Blaschke product is unicritical in the unit disk.

源语言	英语
页（从-至）	1584-1596
页数	13
期刊	Journal of Difference Equations and Applications
卷	23
期	9
DOI	https://doi.org/10.1080/10236198.2017.1341499
出版状态	已出版 - 2 9月 2017

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Epicycloids and Blaschke products

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