On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps  被引量:1

On the Continuity of Julia Sets and Hausdorff Dimension of N CP and Parabolic Maps

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作  者:ZHUANG Wei 

机构地区:[1]Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China

出  处:《Chinese Quarterly Journal of Mathematics》2007年第4期592-596,共5页数学季刊(英文版)

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)).

关 键 词:Julia set Hausdorff dimension Markov partition conformal measure 

分 类 号:O174.51[理学—数学]

 

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