Hausdorff dimension of Julia set of a polynomial with a Siegel disk

Liang Shen

doi:10.1007/s11425-006-1284-1

Hausdorff dimension of Julia set of a polynomial with a Siegel disk

Liang Shen^*

^*此作品的通讯作者

Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

Let f(z) = e^2πiθz(1 + z/d)^d, θ ε ℝ\ℚ be a polynomial. If θ is an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension of the Julia set of f(z) satisfies Dim(J(f)) < 2.

源语言	英语
页（从-至）	1284-1296
页数	13
期刊	Science in China, Series A: Mathematics
卷	49
期	9
DOI	https://doi.org/10.1007/s11425-006-1284-1
出版状态	已出版 - 9月 2006
已对外发布	是

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10.1007/s11425-006-1284-1

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title = "Hausdorff dimension of Julia set of a polynomial with a Siegel disk",

abstract = "Let f(z) = e2πiθz(1 + z/d)d, θ ε ℝ\textbackslash{}ℚ be a polynomial. If θ is an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension of the Julia set of f(z) satisfies Dim(J(f)) < 2.",

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AB - Let f(z) = e2πiθz(1 + z/d)d, θ ε ℝ\ℚ be a polynomial. If θ is an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension of the Julia set of f(z) satisfies Dim(J(f)) < 2.

KW - Hausdorff dimension

KW - Porous set

KW - Siegel disk

UR - https://www.scopus.com/pages/publications/33750202398

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JO - Science in China, Series A: Mathematics

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Hausdorff dimension of Julia set of a polynomial with a Siegel disk

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