Sturmian external angles of primitive components in the Mandelbrot set

Benjamín A. Itzá-Ortiz, Mónica Moreno Rocha, Víctor Nopal-Coello
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Abstract

In this work we introduce the broken line construction, which is a geometric and combinatorial algorithm that computes periodic Sturmian angles of a given period, yielding the locations of their landing parameters in the Mandelbrot set. An easy to implement method to compute the conjugated angle of a periodic Sturmian angle is also provided. Furthermore, if $\theta$ is a periodic Sturmian angle computed by the broken line construction, then we show the existence of a one-to-one correspondence between its binary expansion and its associated kneading sequence.
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曼德勃罗集合中原始成分的斯特尔米外角
在这项工作中,我们介绍了断线构造,它是一种几何和组合算法,可以计算给定周期的周期性斯特尔米安角,并得出它们在曼德尔布罗兹集中的着陆参数位置。还提供了一种易于实现的方法来计算周期性斯图尔缅角的共轭角。此外,如果 $\theta$ 是通过断线构造计算出的周期性斯特角,那么我们证明了它的二进制展开和它的相关捏合序列之间存在一一对应关系。
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