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On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps 被引量:1
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作者 ZHUANG Wei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第4期592-596,共5页
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 ... 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)). 展开更多
关键词 Julia set Hausdorff dimension markov partition conformal measure
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