A note on a quadratic rational map with two Siegel disks

Liang Shen; Sheng Jian Wu

doi:10.1007/s10114-010-6611-3

A note on a quadratic rational map with two Siegel disks

Liang Shen^*
, Sheng Jian Wu

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

Abstract

Suppose f(z) is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim (J(f) < 2.

Original language	English
Pages (from-to)	1393-1402
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	26
Issue number	7
DOIs	https://doi.org/10.1007/s10114-010-6611-3
Publication status	Published - Jul 2010

Keywords

Hausdorff dimension
Porous set
Siegel disk

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10.1007/s10114-010-6611-3

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title = "A note on a quadratic rational map with two Siegel disks",

abstract = "Suppose f(z) is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim (J(f) < 2.",

keywords = "Hausdorff dimension, Porous set, Siegel disk",

author = "Liang Shen and Wu, \{Sheng Jian\}",

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AB - Suppose f(z) is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim (J(f) < 2.

KW - Hausdorff dimension

KW - Porous set

KW - Siegel disk

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M3 - Article

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JO - Acta Mathematica Sinica, English Series

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A note on a quadratic rational map with two Siegel disks

Abstract

Keywords

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