广义M-J集的界与J-集Hausdorff维数的估计

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基金项目: 国家自然科学基金资助项目(699740080);国家博士后基金资助项目

The Bounds of the General M and J Sets and the Estimations for the Hausdorff’s Dimension of the General J Set

1.
Department of Mathematics & Physics, Anshan Institute of Iron & Steel Technology, Anshan 114001, P R China;
2.
School of Information Science and Engineering, Northeastern University, Shenyang 110006, P R China

摘要: 解析地给出了广义M-J集的界,其中某些界在某种意义上是最佳的。解决了应用逃逸时间等算法计算机构造其混沌分形图的首要问题,并在此基础上通过线性逼近的方法给出了某些情况下J-集Hausdorff维数的近似估计。
- 广义Mandelbrot集 /
- 广义Julia集 /
- Hausdorff维数
Abstract: The bounds of the general M and J sets were analytically offered.Some of the bounds were optimal in certain meaning.It not only solved the primary problem of the construction of fractal sets by escape time algorithm,and followed from the conclusion,but also offered two estimations of some special Julia set's Hausdorff’s dimension by approximate linearization method.
- general Mandelbrot set /
- general Julia set /
- Hausdorff’s dimension

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