具有淹没分支的有理函数的性质（英文）

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英文篇名：The Properties of The Rational Maps With Buried Components 作者：庄伟 英文作者：ZHUANG Wei;Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology; 英文关键词：Julia set;;Buried components;;Net;;Hausdorff dimension 中文刊名：SXJK 英文刊名：Chinese Quarterly Journal of Mathematics 机构：Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology; 出版日期：2019-03-30 出版单位：数学季刊(英文版) 年：2019 期：v.34 语种：英文; 页：SXJK201901004 页数：14 CN：01 ISSN：41-1102/O1 分类号：33-46

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 R_n 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 d_H 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.
        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 R_n 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 d_H 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.

引文

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