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中文摘要：
研究了四元数映射z←z2＋c的Mandelbrot集（简称M集）在临界点不为0情况下的结构拓扑不变性和裂变演化规律;计算了M集的周期域边界,探讨了四元数M集周期轨道的拓扑规律.通过在M集中参数c的选择构造了四元数Julia集,定性地分析了四元数M集与Julia集之间的对应关系.实验结果表明,四元数M集临界点不唯一,其分形结构随不同临界点呈现出与以往M集不同的结构特点.
英文摘要：
The quaternion Mandelbrot sets （abbreviated as M sets） on the mapping z←z2＋c with multiple critical points are constructed. The topological invariance and the fission evolutions of M sets are investigated,the stability region boundary is calculated,and the topology rules of the cycle orbits are discussed. The quaternion Julia sets are constructed with the parameter c selected from the M sets and the relationship between the quaternion M sets and the Julia sets are analyzed. It can be concluded that the critical points of quaternion M sets are not unique,which lead the M sets to different fractal structures.
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