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On the Continuity of Julia Sets and Hausdorff Dimension of NCP and Parabolic Maps
Author(s): 
Pages: 592-596
Year: Issue:  4
Journal: CHINESE QUARTERLY JOURNAL OF MATHEMATICS

Keyword:  Julia setHausdorff dimensionMarkov partitionconformal measure;
Abstract: 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 → f horocyclically,then J(fn)→J(f)in the Hausdorff topology,and HD(J(fn))→HD(H(f)).
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