具有淹没分支的有理函数的性质（英文）
The Properties of The Rational Maps With Buried Components作者机构：Department of Mathematics and Physics Beijing Institute of Petrochemical Technology
出 版 物：《Chinese Quarterly Journal of Mathematics》 (数学季刊（英文版）)
年 卷 期：2019年第34卷第1期
页 面：29-42页
主 题：Julia set Buried components Net Hausdorff dimension
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.
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