Non-landing parameter rays of the multicorns
Non-landing parameter rays of the multicorns
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DOI：
10.1007/s00222-015-0627-3
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发表时间：
2014-06
影响因子：
3.1
通讯作者：
H. Inou;S. Mukherjee
中科院分区：
文献类型：
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作者：
H. Inou;S. Mukherjee
众所周知，Mandelbrot集的每个有理参数射线都落在一个参数上。研究了多角形的有理参数射线、单次反全纯多项式的连通性轨迹，并给出了它们的累加性质的完整刻画。主要结果之一是，在多角点的奇周期(周期1除外)双曲分量的边界上积累的参数射线不落在由抛物线参数组成的正长度的弧上。我们还证明了在多角点的边界上存在未修饰的实解析弧，这意味着双曲分量的中心不会在的整个边界上累积，并且Misiurewicz参数在的边界上也不是稠密的。
It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn, the connectedness locus of unicritical antiholomorphic polynomials of degreed, and give a complete description of their accumulation properties. One of the principal results is that the parameter rays accumulating on the boundaries of odd period (except period 1) hyperbolic components of the multicorns do not land, but accumulate on arcs of positive length consisting of parabolic parameters. We also show the existence of undecorated real-analytic arcs on the boundaries of the multicorns, which implies that the centers of hyperbolic components do not accumulate on the entire boundary of, and the Misiurewicz parameters are not dense on the boundary of.