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FANG Li-ping, ZHANG Chun-hong. Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2006, 15(1): 123-126.
Citation: FANG Li-ping, ZHANG Chun-hong. Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2006, 15(1): 123-126.
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Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets

  • School of Science, Beijing Institute of Technology, Beijing 100081, China

Funds:theNationalNaturalScienceFoundationofChina(K10271063)
  • Received Date:2004-09-17
    Abstract
  • More accurate Hausdorff dimension estimations of Julia sets for two simple functions are given by the methods of composition mapping and invariant set of contraction mapping. For quadratic function f c（z）= z2+ c（c∈AC^U）, the range of parameter c is expanded largely and a result on the Hausdorff dimension of its Julia set is gained. Similarly, a better result is obtained for cubic function f c（z）=z3+c（c∈AC^U）.
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