NCP映射与抛物映射的Julia集及其Hausdorff维数的连续性

数学季刊 ›› 2007, Vol. 22 ›› Issue (4): 592-596.

NCP映射与抛物映射的Julia集及其Hausdorff维数的连续性

Department of Mathematics and Physics,Beijing Institute of Petrochemical Technology,Beijing 102617,China

收稿日期:2004-09-01 出版日期:2007-12-30 发布日期:2023-10-23
作者简介:ZHUANG Wei(1968-), male, native of Xintai, Shandong, an associate professor of Beijing Institute of Petrochemical Technology, Ph.D., engages in complex dynamics.
基金资助:

On the Continuity of Julia Sets and Hausdorff Dimension of NCP and Parabolic Maps

Department of Mathematics and Physics,Beijing Institute of Petrochemical Technology,Beijing 102617,China

Received:2004-09-01 Online:2007-12-30 Published:2023-10-23
About author:ZHUANG Wei(1968-), male, native of Xintai, Shandong, an associate professor of Beijing Institute of Petrochemical Technology, Ph.D., engages in complex dynamics.

摘要/Abstract

摘要： Denote by HD(J(f))the Hansdorff dimension of the Julia set J(f)of a rational function f.Our first result asserts that if f is an NCP map,and f_n→f horocyclically, preserving sub-critical relations,then f_nis an NCP map for all n》0 and J(f_n)→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 f_n→f horocyclically,then J(f_n)→J(f) in the Hansdorff topology, and HD(J(f_n))→HD(J(f)).

关键词: Julia set, Hausdorff dimension, Markov partition, conformal measure

Abstract: Denote by HD(J(f))the Hansdorff dimension of the Julia set J(f)of a rational function f.Our first result asserts that if f is an NCP map,and f_n→f horocyclically, preserving sub-critical relations,then f_nis an NCP map for all n》0 and J(f_n)→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 f_n→f horocyclically,then J(f_n)→J(f) in the Hansdorff topology, and HD(J(f_n))→HD(J(f)).

Key words: Julia set, Hausdorff dimension, Markov partition, conformal measure

中图分类号:

O174.51

庄伟. NCP映射与抛物映射的Julia集及其Hausdorff维数的连续性[J]. 数学季刊, 2007, 22(4): 592-596.

ZHUANG Wei . On the Continuity of Julia Sets and Hausdorff Dimension of NCP and Parabolic Maps[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(4): 592-596.

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