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