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^*

^*Corresponding author for this work

Peking University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1284-1296
Number of pages	13
Journal	Science in China, Series A: Mathematics
Volume	49
Issue number	9
DOIs	https://doi.org/10.1007/s11425-006-1284-1
Publication status	Published - Sept 2006
Externally published	Yes

Keywords

Hausdorff dimension
Porous set
Siegel disk

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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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author = "Liang Shen",

year = "2006",

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N2 - 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.

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

U2 - 10.1007/s11425-006-1284-1

DO - 10.1007/s11425-006-1284-1

M3 - Article

AN - SCOPUS:33750202398

SN - 1006-9283

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EP - 1296

JO - Science in China, Series A: Mathematics

JF - Science in China, Series A: Mathematics

IS - 9

ER -

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

Abstract

Keywords

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