Better Hausdorff Dimension Estimations of Quadratic and Cubic Functions' Julia Sets

摘要

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) = z~2 + c(c ∈ C), 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) = z~3 + c(c ∈ C).