具有淹没分支的有理函数的性质
录用日期: 2017-03-14
网络出版日期: 2020-10-06
The Properties of The Rational Maps With Buried Components
Accepted date: 2017-03-14
Online published: 2020-10-06
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 Rn→ R algebraically, and Rn and R topologically conjugate for all n >> 0, then Rn is an NCP map with buried components for all n >> 0, and for some C > 0,dH（J（R）, J（Rn）） ≤ C（dist（R,Rn)1/d,where dH denotes the Hausdorff distance, and HD（J（Rn）） → 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 Ji（R） is either a real-analytic curve or HD（Ji（R）） > 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 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.004
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 Rn→ R algebraically, and Rn and R topologically conjugate for all n >> 0, then Rn is an NCP map with buried components for all n >> 0, and for some C > 0,dH（J（R）,J（Rn）） ≤ C（dist（R, Rn)1/d,where dH denotes the Hausdorff distance, and HD（J（Rn）） → 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 Ji（R） is either a real-analytic curve or HD（Ji（R）） > 1.
Key words： Julia set; Buried components; Net; Hausdor? dimension
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