关于抛物有理函数的Hausdorff维数与共形测度的相等性

数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 206-213.

关于抛物有理函数的Hausdorff维数与共形测度的相等性

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology

收稿日期:2011-09-23 出版日期:2013-06-30 发布日期:2023-03-01
作者简介:ZHUANG Wei(1968-), male, native of Xintai, Shandong, an associate professor of Beijing Institute of Petrochemical Technology, engages in complex dynamics.

On the Equality of Hausdorﬀ Dimensions and Conformal Measures of Parabolic Maps

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology

Received:2011-09-23 Online:2013-06-30 Published:2023-03-01
About author:ZHUANG Wei(1968-), male, native of Xintai, Shandong, an associate professor of Beijing Institute of Petrochemical Technology, engages in complex dynamics.

摘要/Abstract

摘要： Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), m_g = m_foh^-1 .

关键词: Julia set, net, conformal measure, Hausdorff dimension

Abstract: Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), m_g = m_foh^-1 .

Key words: Julia set, net, conformal measure, Hausdorff dimension

中图分类号:

O174.51

庄伟. 关于抛物有理函数的Hausdorff维数与共形测度的相等性[J]. 数学季刊, 2013, 28(2): 206-213.

ZHUANG Wei. On the Equality of Hausdorﬀ Dimensions and Conformal Measures of Parabolic Maps[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 206-213.

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