摘要
Denote by HD（J（f）） the Hausdorff dimension of the Julia set J（f） of a rational function f. Our first result asserts that if f is an NCP map, and fn → f horocyclically,preserving sub-critical relations, then fn is an NCP map for all n ≥≥ 0 and J（fn） →J（f） in the Hausdorff topology. We also prove that if f is a parabolic map and fn is an NCP map for all n ≥≥ 0 such that fn→4 f horocyclically, then J（fn） → J（f） in the Hausdorff topology, and HD（J（fn）） →4 HD（J（f））.
