| 牛顿变换Julia集的对称性 |
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| 引用本文： | 阳卫锋.牛顿变换Julia集的对称性[J].纯粹数学与应用数学,2009,25(3):530-533. |
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| 作者姓名： | 阳卫锋 |
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| 作者单位： | 湖南工程学院数理系,湖南,湘潭,411104 |
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| 摘 要： | 主要讨论多项式的牛顿变换Julia集的对称性问题．利用复动力系统理论，证明了多项式P（z）的Julia集的对称群是其牛顿变换Np（z）的Julia集的对称群的子群．获得了Julia集为一水平直线的充分必要条件．
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| 关 键 词： | 牛顿变换 Julia集 对称群 共形欧氏变换 |
Symmetries of the Julia sets for Newton's method |
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| YANG Wei-feng.Symmetries of the Julia sets for Newton's method[J].Pure and Applied Mathematics,2009,25(3):530-533. |
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| Authors: | YANG Wei-feng |
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| Institution: | YANG Wei-feng (Department of Mathematics Physics,Hunan Institute of Engineering,Xiangtan 411104,China) |
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| Abstract: | The symmetries of Julia sets of Newton＇s method is investigated. Using the theory of complex Dynamical system, it is shown that the group of symmetries of Julia sets of polynomial is a subgroup of that of the corresponding Newton＇s method. A necessary and sufficient condition for Julia sets of Newton＇s method to be a horizontal line is arrived. |
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| Keywords: | Newton＇s method Julia set group of symmetries conformal Euclidean isometry |
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