The main cubioid
The main cubioid
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DOI：
10.1088/0951-7715/27/8/1879
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发表时间：
2013-05
期刊：
影响因子：
1.7
通讯作者：
A. Blokh;L. Oversteegen;R. Ptacek;V. Timorin
中科院分区：
文献类型：
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作者：
A. Blokh;L. Oversteegen;R. Ptacek;V. Timorin
二次多项式的参数空间中的连通性轨迹称为Mandelbrot集。一个很好的组合模型，这一套是由于瑟斯顿。根据定义，Mandelbrot集的主双曲域由参数值组成，对应的二次多项式具有吸引不动点。Mandelbrot集的主双曲域的闭包称为主心形线。其拓扑结构完全由Thurston模型描述。关于三次多项式参数空间中的连通性轨迹的研究知之甚少。在本文中，我们讨论了三次类似的主要心脏线，并建立它们之间的关系。
The connectedness locus in the parameter space of quadratic polynomials is called the Mandelbrot set. A good combinatorial model of this set is due to Thurston. By definition, the principal hyperbolic domain of the Mandelbrot set consists of parameter values, for which the corresponding quadratic polynomials have an attracting fixed point. The closure of the principal hyperbolic domain of the Mandelbrot set is called the main cardioid. Its topology is completely described by Thurston's model. Less is known about the connectedness locus in the parameter space of cubic polynomials. In this paper, we discuss cubic analogues of the main cardioid and establish relationships between them.