具有淹没分支的有理函数的性质

doi:10.13371/j.cnki.chin.q.j.m.2019.01.004

数学季刊 ›› 2019, Vol. 34 ›› Issue (1): 29-42.doi: 10.13371/j.cnki.chin.q.j.m.2019.01.004

具有淹没分支的有理函数的性质

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology

接受日期:2017-03-14 出版日期:2019-03-30 发布日期:2020-10-06
作者简介:ZHUANG Wei(1968-05), male, native of Xintai, Shandong, vice-professor of Beijing Institute of Petrochemical Technology, Beijing, China, engages in Complex Dynamics.

The Properties of The Rational Maps With Buried Components

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology

Accepted:2017-03-14 Online:2019-03-30 Published:2020-10-06
About author:ZHUANG Wei(1968-05), male, native of Xintai, Shandong, vice-professor of Beijing Institute of Petrochemical Technology, Beijing, China, engages in Complex Dynamics.

摘要/Abstract

摘要：

Let R（z） be an NCP map with buried components of degree d = degf ≥ 2 on the complex sphere ■, and HD denotes the Hausdorff dimension. In this paper we prove that if R_n→ R algebraically, and Rn and R topologically conjugate for all n >> 0, then R_n is an NCP map with buried components for all n >> 0, and for some C > 0,d_H（J（R）, J（R_n）） ≤ C（dist（R,R_n)^1/d,where dH denotes the Hausdorff distance, and HD（J（R_n）） → HD（J（R））.In this paper we also prove that if the Julia set J（R） of an NCP map R（z） with buried components is locally connected, then any component J_i（R） is either a real-analytic curve or HD（J_i（R）） > 1.

关键词: Julia set, Buried components, Net, Hausdor? dimension

Abstract:

Let R（z） be an NCP map with buried components of degree d = degf ≥ 2 on the complex sphere ■, and HD denotes the Hausdorff dimension. In this paper we prove that if R_n→ R algebraically, and Rn and R topologically conjugate for all n >> 0, then R_n is an NCP map with buried components for all n >> 0, and for some C > 0,d_H（J（R）,J（R_n）） ≤ C（dist（R, R_n)^1/d,where dH denotes the Hausdorff distance, and HD（J（R_n）） → HD（J（R））.In this paper we also prove that if the Julia set J（R） of an NCP map R（z） with buried components is locally connected, then any component J_i（R） is either a real-analytic curve or HD（J_i（R）） > 1.

Key words: Julia set, Buried components, Net, Hausdor? dimension

中图分类号:

O186.1

庄伟. 具有淹没分支的有理函数的性质[J]. 数学季刊, 2019, 34(1): 29-42.

ZHUANG Wei. The Properties of The Rational Maps With Buried Components[J]. Chinese Quarterly Journal of Mathematics, 2019, 34(1): 29-42.

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具有淹没分支的有理函数的性质

The Properties of The Rational Maps With Buried Components

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